MILITARY THOUGHT No. 7/2009, pp. 12-20

Simulation of armed confrontation: development prospects

Colonel IN AND. GRAZING,

candidate of military sciences

Colonel D.B. KALINOVSKY

Colonel O. V. TIKHANYCHEV,

Candidate of Technical Sciences

AT THE PRESENT, the role and importance of military-scientific substantiation of decisions of state and military command and control bodies in the field of construction, training, planning the use and management of the Armed Forces is significantly increasing in the course of solving the tasks facing them to ensure the military security of the state. At the same time, as the experience of local wars and armed conflicts shows, the most important conditions for successfully achieving the goals of modern operations are timely tracking and display in near real time of the situation in conflict zones, forecasting its development, elaboration of various options for actions of the troops of the parties, including including using mathematical modeling methods.

The relevance of the problem of applying mathematical modeling methods in military affairs is confirmed by a large number of publications on this topic in various periodicals. Their analysis shows that the opinions of the authors vary, ranging from complete rejection of mathematical models in military affairs to a completely objective understanding of this issue, although with certain reservations.

The reasons for this range of opinions are varied. Some people believe that calculation tasks and a mathematical apparatus for comparing combat potentials are sufficient to provide information support for planning an operation; others insist on using simplified models, relying on the commander’s ability to “build a mental model of the upcoming battle and operation,” or simply do not distinguish between models and calculation problems, interpreting their definitions quite freely.

Although almost all authors talk about the need for forecasting in the work of commanders (commanders) and staffs, very often there is an opinion, confirmed, at first glance, by well-founded examples and reasoning, that the use of mathematical modeling methods is inappropriate and sometimes dangerous, since it leads to a distortion of the assessment planning results. In our opinion, there are several reasons for this misconception. This is, firstly, a lack of understanding of the essence of mathematical modeling, the purpose of the models used, their capabilities, the assumptions taken when developing and the boundaries of application. Secondly, putting forward the same operational and technical requirements for models and tasks for various purposes, used for different levels of management. And finally, thirdly, the unreasonable “absolutization” of the modeling results.

All this is a consequence of different understandings of the problem of modeling armed confrontation by military theorists and officials of military command and control agencies. To discuss this issue reasonably, It is necessary first of all to determine its main components: terminology of mathematical modeling; classification of mathematical models and forecasting methods; methodology and boundaries of application of mathematical models; technologies for implementing mathematical models for various purposes.

First of all, you should understand what to count mathematical model(MM) what information and calculation task(IRZ), and also how it differs math modeling from carrying out operational-tactical calculations(OTR). In the reference literature there is a fairly large number of definitions of the concepts under consideration.

So, in the “Military Encyclopedia” mathematical model is interpreted as a description of a phenomenon (object) using mathematical symbols. In the "Military Encyclopedic Dictionary" math modeling in military affairs it is formulated as a method of military-theoretical or military-technical research of an object (phenomenon, system, process) by creating and studying its analogue (model) in order to obtain information about the real system.

Operational-tactical calculations in the same dictionary are described as calculations carried out by the personnel of departments, formations, formations, units and subunits, the purpose of which is to determine quantitative, qualitative, time and other indicators for making decisions on an operation (battle) or justifying planning for the use of troops and ensuring control.

One of the most popular electronic Internet encyclopedias, Wikipedia, gives its formulations of concepts related to mathematical modeling. So, task in the most general “canonical” form - a logical statement like: “given given conditions, it is required to ensure the achievement of a certain goal,” and model - a logical or mathematical description of components and functions that reflect the essential properties of the object or process being modeled.

Based on the definitions given in the same source, one can clearly see the significant difference between an individual mathematical model, a complex and a system of models. Set of models - a set of models designed to solve one complex problem, each of which describes one or another aspect of the modeled object or process. If the models are connected in such a way that the results of some turn out to be the initial data for others before obtaining a common result, then the complex turns into a system of models. Model system - a set of mutually related mathematical models to describe complex systems that cannot be reproduced in one model. To plan and predict the behavior of large objects, systems of models are developed, usually built on a hierarchical principle, V several levels. They are called multi-level systems.

And finally, the current GOST series “RV” provides the following definitions of the mathematical model and calculation problem. Mathematical model of operation (combat)- a system of mathematical dependencies and logical rules that allows one to reproduce in time the most significant components of simulated combat operations with sufficient completeness and accuracy and, on the basis of this, calculate the numerical values ​​of the indicators of the predicted course and outcome of military operations.

Calculation problem - a set of mathematical dependencies, algorithms and data for performing operational-strategic (operational-tactical) or special calculations, allowing one to assess the situation that will arise as a result of the proposed actions or calculate control parameters that ensure the achievement of the required result with a probability not lower than the specified one.

Analysis of these definitions shows the difference between MM and IRD, which consists in the fact that the former are intended to predict the development of the situation under different variants of the initial data, and the latter are primarily intended to carry out direct calculations in the interests of obtaining a specific result. Earlier IRZ were solved mainly by hand, and MM- on “mainstream” computers. With the development of automation tools, many tasks were transferred in the form of programs to COMPUTER, which made it possible to complicate the mathematical apparatus used, the number of factors taken into account, and led to some “blurring” of the line between MM and IRD. This, in our opinion, is one of the reasons for misunderstandings regarding the use of mathematical modeling in the course of operational-tactical calculations.

In accordance with the governing documents, the main functions of headquarters are collecting information and assessing it, planning an operation (battle) and forecasting changes in the situation. With planning, everything is quite clear: it primarily involves solving direct and reverse IRDs. But to assess the situation, predict its changes, as well as for a comparative assessment of the planned options for the use of troops (forces), the use of various mathematical forecasting methods is required (Fig.).

Classification of forecasting methods

Each of these methods has been tested in various areas of management activity and has proven its right to exist. But not all of them can be used in the practical activities of commanders (commanders) and staffs when organizing military operations. This is due to the peculiarities of warfare, which consist in the significant uncertainty of the initial data, the need to take into account a huge number of factors and the high “cost” of erroneous decisions. Based on this, methods of extrapolation of trends and some types of models are almost never used in organizing military operations. Expert methods and mathematical modeling are a different matter, but their application is also significantly influenced by the above features.

Formally, any of the approaches to forecasting shown in the figure can be attributed to modeling processes and identifying trends: logical, mental, mathematical. But based on the specifics of modeling armed confrontation, the definition of MM used in GOSTs of the “RV” series, it is advisable, when talking about modeling, to consider mathematical models that describe the processes of armed confrontation, its components and individual forms. Below we will talk mainly about such models.

The classification of mathematical models affects the requirements for them, the formation of lists of MM and IRZ, which provide decision support for officials of military command and control agencies. According to their purpose, MMs are usually divided into research and staff (Table 1).

Table 1

Classification of mathematical models

Research models are intended both to support research related to the development of weapons, the development of new methods of conducting operations and combat operations, and to analyze the results of calculations during advance planning. The main requirement for them is to ensure the necessary accuracy of the mathematical description of the processes under study. Less stringent requirements are imposed on the efficiency of modeling.

Staff models are mathematical models of operations (combat actions) designed to support the practical activities of headquarters. They are presented two basic requirements: first - the possibility of application in real time, fitting into the algorithm of the headquarters; the second is to ensure a significant increase in the objectivity and validity of decisions made regarding the command and control of troops.

According to the form of description of the process of armed confrontation, MM are divided into analytical And stochastic. Both of them can be both staff and research.

According to the obtained modeling result, the models are most significantly divided into straight(describing) and prescriptive(optimizing or prescriptive). The first ones allow you to answer the question: “what will happen if...”, the second ones: “how to make it happen like this.” Descriptive models are most often used in military affairs. The use of prescriptive models, which are more promising from the point of view of decision support, is hampered by a number of objective and subjective factors.

Objective is that with a large number of factors taken into account, it is very difficult to formulate a formal problem of finding an optimal solution. It is equally difficult to interpret the results obtained. Subjective factors: the reluctance of officials to trust the search for a solution to a program whose operating principles are unknown to them. There is also an opinion that the algorithm of the prescriptive model can be calculated, and, knowing it, the result of the decision can be calculated. This opinion is undoubtedly erroneous, since even with a known algorithm for the model’s operation, it is impossible to calculate the result of the simulation without having accurate information about the initial data entered into the model.

It is difficult to judge how significant these factors are for the development of MM, but the fact is clear: currently for forecasting in the military field, descriptive models are used. This trend is likely to continue in the near future.

Some sources, discussed at the beginning of the article, express the opinion that modeling (and sometimes forecasting) can be replaced by direct calculations; it is enough to describe the process with a varying degree of approximation by a system of equations. However, there is a subtle but dangerous pitfall in this approach. Firstly, some processes are simply impossible to describe explicitly. Secondly, describing the behavior of a system with equations in explicit form requires the introduction of a significant number of correction and generalizing coefficients, most of which are obtained empirically by generalizing the statistics of known events. This is done under strictly specified conditions, which the potential user of the settlement system will not know about at the time of making the decision. Any change in the forms, methods, or means of armed struggle reduces the accuracy of the system of equations and distorts the solution of the problem. That's why Calculation methods will never replace a model operating with probabilistic approaches.

The boundaries of the application of mathematical modeling, the list of applied MMs within the framework of the above classification are determined by the forecasting and assessment problems solved in the military command and control bodies using them, as well as the capabilities of providing input and the needs for output information of the models. From the analysis of the requirements of the main governing documents and the experience of operational training activities, it is possible to determine the needs of military command and control bodies in the use of mathematical models and present their hierarchical structure (Table 2).

The proposed classification is not a dogma, but only reflects the needs of military command and control bodies for means of calculation and information (in the long term and intellectual) support and justification of decisions made. The implementation of the proposed models at management levels, their multi-link interconnection, is essentially the prospect for the development of mathematical modeling.

Despite the objective need to use mathematical models in organizing military operations, their use is significantly influenced by subjective factors associated with the attitude of officials to the modeling results. It should be clearly understood that the model is not a means of directly developing decisions on the use of troops (forces) or justifying ways of developing a weapons system, but only a tool that ensures the implementation of one of the stages of this process - a comparative assessment of the quality of decisions made. This tool is developed for specific tasks and conditions with certain assumptions and has a corresponding scope. Moreover, it is not always possible and necessary to develop a certain universal model; it is often more expedient to have a set of tools used to solve specific problems at certain workplaces (management levels), adapted to specific working conditions. Only such an understanding will make it possible to formulate the correct approach to the use of model technologies in military command and control agencies and bring the organization of military operations (operations, combat actions) of the RF Armed Forces to a qualitatively new level that meets the requirements of warfare modern warfare level.

In this regard, as well as from the point of view of technological implementation of model technologies, the most appropriate classification of mathematical models regarding their inclusion in the composition of special mathematical and software(SMPO) automated troop control systems (ATCS). With this approach, models can be implemented, firstly, directly as part of the SMPO automation equipment complexes(KSA) ACCS; secondly - in the form of separate software and hardware systems(PTK), providing solutions to specific problems; thirdly - as part of stationary or mobile multifunctional modeling centers(computer centers for modeling military operations - CC MIA).

Experience in the development and operation of automated control systems shows that in a number of cases there is the objective need to include mathematical models in the SMPO ASUV, for example, to provide a comparative analysis of options for the use of troops when developing an operation plan, assessing the effectiveness of options for constructing a massive fire strike, etc. Mathematical models operating as part of special software (SPO) of the automated control system must ensure automated exchange of information with the system database, other models and tasks, receiving most of the information from them in an automated manner. These models must have an extremely simple user interface that provides a sufficient set of formalized control actions for the order of use of troops (forces) and combat systems, as well as functions for a visual presentation of modeling results.

table 2

Hierarchical structure of mathematical models of armed

confrontation

We are talking primarily about staff models, sometimes also called “express models” in the specialized literature, although the definition of “express” sounds somewhat pejorative, reflecting only the external consumer qualities of the model - ease of control and speed of obtaining results. At the same time, staff models are quite complex products: they adequately describe the process for which they were developed to model. External simplicity is achieved by long-term work on optimization of computational algorithms and user interfaces. But it is precisely these models that can be widely used by officers who do not have special computer training.

To be fair, it should be noted that creative and “piecemeal” work on creating program interfaces and developing approaches to unify them, which can only be performed by a specialist with a broad operational and technical outlook, does not belong to scientific activity. At the same time, the lack of unified approaches to the interface implementation of mathematical models and information and calculation tasks in the work of officials significantly reduces their user properties, making it difficult for officials to master and implement them in the activities of military command and control bodies.

Models that are more diverse in functionality, although more complex to operate, are sometimes advisable not to be included in the ACS V SMPO, but to be used as part of multifunctional computer modeling centers or separate specialized hardware systems. This is due to the following factors:

complex models, complexes and systems of models can form computer requirements, not always provided by means of serial automated control systems;

the high cost of development and the need to maintain complex mathematical models sometimes makes it impractical to supply them to military command authorities for use only a few times a year, and sometimes less often, it is more expedient use one model in move mode as part of mobile hardware systems with its own personnel;

more complex and diverse models require maintenance more trained specialists, which are not always available in automated military command and control bodies;

requirements for the composition and detail of the initial data of complex models (complexes and systems of models) do not always allow them to be organized automated interaction with the ACCS database;

variety of output information requires it comprehensive assessment, often bordering on science and art, which can only be achieved by an experienced modeling specialist. Moreover, only a specialist in the field of modeling can know in detail the assumptions and limitations adopted during the development of the model, the scope of its application and assess the degree of influence of these factors on the modeling results. In the matter of operational (combat) planning, given the high cost of a mistake, this is an important circumstance.

These factors, combined with the need to ensure solutions to the problems of operational planning and the formation of a weapons program, necessitate the creation of specialized computer centers (separate PTCs) for modeling military operations (CC MVD) outside the framework of the automated control system. Such computer simulation centers can be stationary or mobile, equipped with computers in various configurations, but at the same time, the conditions for the possibility of exchanging information between the CC of the Ministry of Internal Affairs and the automated control system and ensuring the requirements for the safety of the initial information of the automated control system must be met.

Stationary modeling centers can be used in the interests of senior management bodies when carrying out strategic planning, organizing and analyzing the results of operational training activities, forming weapons programs, developing mobilization plans and carrying out other similar activities.

Mobile CCs of the Ministry of Internal Affairs can be used to strengthen the headquarters of operational-strategic and operational units during operational planning and advance preparation of operations, as well as during operational (combat) training activities.

Thus, mathematical modeling in the field of armed confrontation is advisable, in our opinion sight, develop in the following main areas:

First - creation of staff models that take into account the main factors influencing the process of confrontation, with an extremely simple interface for use as part of the automated control system software when conducting a comparative assessment of decisions on the use of troops (forces). Along with this, it is possible to consider the possibility of introducing models into calculation and modeling complexes in order to conduct a comparative assessment of the calculated options automatically, unnoticed by the user.

Second - creation of specialized hardware systems, including mobile ones, interfaced with automated control system automated control system for input and output data, for modeling in the interests of solving complex problems and problems with limited access to information.

Third - creation outside the framework of automated control systems of multifunctional control centers of the Ministry of Internal Affairs, including complexes and systems of mathematical models and calculation problems in order to ensure the solution of a wide range of problems of assessing and forecasting the situation in the interests of making military-political decisions, planning military operations and building the Armed Forces.

The proposed classification of models, the proposed conceptual apparatus and approaches to the implementation of MM for military command and control bodies at various levels will allow, in our opinion, to clearly define the place and principles of using mathematical modeling technologies in the RF Armed Forces, to develop a unified view on the methods of using MM in the construction system, planning application , training and command and control of troops (forces), streamline the process of their development and implementation into practice of the activities of military command and control bodies.

An analysis of the state, prospects for the development of modeling and the dynamics of growth in costs for the development of mathematical models of military operations in the armed forces of the leading states of the world shows the seriousness of this issue abroad and serves as additional confirmation of the relevance of the issues discussed in this article.

Military Thought. 2004. No. 10. P. 21-27; 2003. No. 10. P. 71-73.

Military Thought. 2007. No. 9. P. 13-16; 2007. No. 10. P. 61-67; 2008. No. 1. P. 57-62.

Military Thought. 2005. No. 7. P. 9-11; 2006. No. 12 P. 16-20.

Military Thought. 2007. No. 10. P. 61-67; 2007. No. 9. P. 13-16; 2008. No. 3. P. 70-75.

Military Encyclopedia. M.: Voenizdat, 2001. T. 5. P. 32.

Military encyclopedic dictionary. M.: Ministry of Defense of the Russian Federation, Institute military history, 2002. P. 1664.

http://www.wikipedia.org._

Foreign military review. 2006. No. 6. P. 17-23; 2008. No. 11. P. 27-32.

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MILITARY THOUGHT No. 12/1987, pp. 36-44

TROOPS MANAGEMENT

B. A. KOKOVIXIN ,

reserve rear admiral, candidate of naval sciences, associate professor

The article expresses the purely personal opinion of the author. We invite readers to express their views on the issues discussed in it.

THIS article discusses the issue of creating mathematical models (methods) to justify by calculations the decisions made by commanders during the preparation and conduct of combat operations. In principle, this problem has existed throughout the history of wars and military art, but it became most acute in the 20th century due to the emergence and rapid development of new types of weapons and equipment. Currently, the goal is to create mathematical models that could better support the practical activities of commanders and their staffs.

Due to a number of circumstances, this problem has not yet been completely solved. For a long time it was believed that the main difficulties and failures in solving it were due to insufficient capabilities of computer technology and mathematics. At the current level of their development, this point of view becomes unconvincing and untenable. Now priority attention is paid to the methodological side of the problem. Therefore, first of all, it is necessary to reveal, analyze and eliminate the reasons that make it difficult to create practical models of operations (combat actions). In my opinion, the first (main) reason lies in the field of basic concepts (categories) of the theory of war and military art, and therefore, first of all, it is important to know exactly what armed struggle and its constituent military actions are, called a strike, battle, battle, operation , what is their essence, internal, objectively necessary content and structure, how they are interconnected, how they differ from each other.

Unfortunately, it seems to me that there are no clear, logical, and logical answers to these questions. For example, the theory defines “combat actions” as follows: 1) organized actions of units and formations of all types of aircraft in the performance of assigned combat missions. The term “military actions” is usually applied to combat operations of an operational-strategic and strategic scale; 2) the form of operational use of formations and formations of aircraft types within an operation (or between operations) as part of a larger-scale formation. Varieties of combat operations are systematic combat operations as a special form of operational use of air defense, air force, and naval formations. These unclear, contradictory, defying logical explanation definitions, in my opinion, are generated by a large-scale classification, according to which the actions of troops are usually divided into combat, operational and strategic not depending on their essence and objectively necessary content, but “depending on the scale of the armed struggle, capabilities of troops (forces), goals and nature of combat missions.”

The question arises: is it possible to develop practically acceptable mathematical models without operating with sufficiently accurate and deep basic concepts (categories) of military art? Actually, it’s possible. But where does this lead? Many years have passed, a lot of effort and money have been spent, but the problem has not found its complete theoretical and practical solution. Moreover, sometimes the question is raised whether research is being conducted in the right direction. If the necessary models are created without strict and deep theoretical justification, the results obtained with their help will not deserve complete confidence. “You cannot move forward successfully through trial and error. This comes at a cost to society." Consequently, in order to ensure a reliable, theoretically based solution to the problem, it is first of all necessary to clarify and deepen our concepts about the essence, content, structure of armed struggle, and the components of the art of war.

This is required.

First. Firmly adhere to the Marxist-Leninist definition of war as an organized armed struggle between states or classes within a state, which by its socio-political nature is “the continuation of politics by violent means.” “Violence is currently the army and navy...” (K. Marx And F. Engels. Soch., vol. 20, p. 171). Political, economic, ideological and other forms of struggle not only do not stop, but, on the contrary, become fiercer during a war, ultimately exerting a decisive influence on its outcome, which, however, does not change the essence and objectively necessary content of war as an armed struggle. The definition of war given in the Soviet Military Encyclopedia as the totality of all forms of struggle, including armed, repeats the outdated point of view that existed back in early XIX century. I believe that such a definition distorts reality, introduces confusion into the understanding of the subject of military science, and makes it difficult to solve theoretical and applied problems, including modeling operations (combat actions). Historical experience confirms that military science has always been and is engaged in war as armed struggle and military art, and therefore the theory of war and military art is actually “military” science, its philosophical (fundamental) part.

Second. Separate the theory of war and military art from theoretical descriptions of standard options for waging war and military operations, depending on the prevailing conditions of the military-political situation in the world and the views of the military leadership of the opposing sides. The fact is that standard options and views in the form of statutory provisions have been replaced military science. The officer corps of the command and staff specialty studies, works, and trains subordinates not according to science, but according to their views; the actions of our troops are organized according to our views, the enemy is assessed according to his views. All this inevitably leads to the adoption of template decisions that cannot fully ensure the development of mathematical models acceptable to headquarters.

Third. The training of officers and persons involved in modeling military operations must begin with proving the truth (correspondence to objective reality) of the categories of military science, just as, for example, theorems are proven in geometry. V.I. Lenin emphasized: “Categories must withdraw(and not arbitrarily or mechanically take) (not “telling”, not “assuring”, but proving)..."(Poln. sobr. soch., vol. 29, p. 86). This will allow students to simultaneously understand the essence of methods of strategic, operational, combat operations and the theory of military art in general.

In the work “Categories of Military Art in the Light of Materialist Dialectics,” an attempt is made to derive the categories of war and military art, to clarify and bring them into an interconnected system, and to formulate the following basic provisions.

Actions of troops (forces) in war (“military” actions) include deployment, redeployment and creation of groupings: in the theater of war- to conduct interrelated operations (“strategic” actions); in surgery- for conducting interconnected battles (“operational” actions); in battle- for the interconnected use of weapons, as well as their very use against the enemy (“combat” actions). Consequently, in modern conditions, when waging war only with conventional weapons hostilities- is a set of strategic, operational and combat (tactical) actions. In principle, they can be carried out by any number of troops, but it is advisable to limit their upper limit to such a number, with a further increase in which the probability of completing the assigned task remains practically at the same level.

The armed struggle and the military actions that make it up are not conducted in general, as anyone wants, but in objectively necessary ways, which are battle, operation, regrouping, military action. Way- these are the actions of troops of a given composition organized in a certain way when performing a given task in the specific conditions of the current situation. Military actions, no matter what they are called, are nothing more than a manifestation of the essences of the main methods in their various combinations. Moreover, the actions of the troops of both one and the other side during the war continuously transform into each other in a strictly defined sequence that cannot be changed. Their essence lies in uniting and concentrating the efforts and capabilities of the troops where and at the moment where and when it is necessary. In combat, this is achieved by combining firepower to destroy those enemy objects (groups), the destruction (incapacitation) of which ensures the completion of the assigned task. This path allows you to significantly increase the overall force of the attack or resistance of troops, in relation to the arithmetic sum of the individual capabilities of combat units to create the necessary superiority over the enemy and defeat him. In operation- combining the final results of the actions of troops in all battles that make up a given operation, to defeat those enemy groups and objects, the destruction of which ensures the completion of the assigned task.

In this case, it is assumed not only to defeat selected targets, but also to use the results of the troops’ actions in some battles to increase their effectiveness in others. When regrouping on a theater of operations - by deploying and re-deploying troops with their comprehensive support in order to timely create fully trained groups to conduct operations in a decisive place and at the decisive moment of the war; in war - by uniting and using in mutual interests the final results of the actions of troops in all operations aimed at defeating the enemy’s armed forces in a given theater of military operations, as well as through the timely creation of comprehensively supported groups to conduct planned operations.

Based on the foregoing, we can say that for the practical activities of commanders (commanders) and their staffs, it is necessary to develop mathematical models of methods of conducting combat (operations) based on the qualitative and quantitative composition of troops that are allocated or can be allocated to perform the assigned task, taking into account the internal structure war and military art (diagram 1). When creating them, it is also important to take into account the natural-historical process of development and change in methods of warfare, its constituent military actions, depending on the emergence and development of new types of weapons and technical means (Diagram 2).

Fourth. The theory of war and military art, i.e. the philosophical (fundamental) part of military science, must be removed from narrow departmental subordination and transferred to the USSR Academy of Sciences, where it must be represented on an equal basis with all other social sciences. This, in my opinion, is the only real way that can raise military science to a higher, qualitatively new level, providing a reliable, theoretically based solution to many applied problems, including modeling military operations.

The second reason for the difficulties in developing models is that now they are required to take into account, if possible, all the factors that may influence the organization and conduct of an operation (combat operations). This inevitably leads to a sharp increase in unpredictable initial information. Such models can be used only for research purposes, but not for the work of commanders (commanders) and staffs when planning military operations.

Currently, models are developed in advance and represent a mathematical analogue of a typical battle (operation), which takes into account to the maximum extent possible: the existing organizational structure of troops (forces), their regular quantitative and qualitative composition; typical parameters of various military actions recorded in governing documents; specific military-geographical conditions of theaters of military operations, etc. Moreover, this applies to both our troops and the enemy. In life, specific military actions never completely coincide with typical ones. Considering that the organization, staffing of troops (forces) and other conditions are constantly and rapidly changing, the developed models also lose their practical value. This is the third reason.

The fourth is that specialists in the field of military art (operators) actively participate in the creation of standard mathematical models of military operations, modeling them only in the part that concerns the development of a verbal model in the form of formulating possible solutions for the warring parties. Initial information is laid down in advance. The missing part, necessary for the model to “work” in a specific situation, is periodically refined and selected from the so-called constant information.

The general disadvantage of staff models is that with their help it is possible to evaluate only one side of the military art of the commander (commander) making a decision, which characterizes his ability to organize the actions of troops in order to maximize the use of their potential capabilities. The second (from the point of view of military art, the more complex and difficult side) is the use and, if possible, the creation (by misleading the enemy, rapid and unexpected maneuver of troops, etc.) conditions that make it possible to weaken the enemy and significantly increase the combined efforts of friendly forces. troops in the main direction at the decisive moment of the battle (operation) is poorly assessed by existing models.

Based on the above provisions regarding the theory of war and the art of war, I propose one of the possible approaches that can ensure the creation of mathematical models of military operations that are practically acceptable for headquarters. Its essence boils down to the following.

Each battle (operation) model must be clarified by the corresponding commander (commander) and his staff on the basis of the information that they have during the development and decision-making period, while determining only the plans of action of the opposing sides.

Why only plans?

Historical experience shows that the actual course of military operations usually corresponded precisely to the plans of the parties’ actions and never completely coincided with detailed decisions (plans), regardless of which side (attacking or defending) achieved or failed to achieve its goal. For example, the Nazi army, whose military leaders were meticulous, especially when planning a surprise attack, successfully launched a war against Soviet Union and led it in 1941 in accordance with the plan underlying the Barbarossa plan. However, the subsequent course of events differed significantly from the plan. Ultimately, the goal of the war was not achieved due to the insufficient justification of its plan: the unity, cohesion of the Soviet people and the unparalleled heroism of our soldiers were not taken into account.

Thus, a model developed on the basis of information describing in detail the upcoming course of military operations of the parties will obviously not correspond to the actual course of events, and the results of the calculations will be very doubtful. When applying the proposed approach, it is important that in the formulation of the plans of the parties’ actions, the essence of the art of war is clearly visible, which, in my opinion, lies in the ability to become stronger than the enemy, to create overwhelming superiority over him at the decisive moment and in the decisive place of the war and its constituent military actions. (Here we are not talking about creating overall military superiority on a global scale, which is what the United States of America is striving for, but about the art (ability) to defeat the aggressor with the available forces in the event of an attack). Understanding this is the basis that unites strategy, operational art and tactics in a dialectical unity. At the same time, each component of military art has its own essence. But, in my opinion, the essence of strategy, operational art and tactics lies in the ability to create overwhelming superiority over the enemy at a decisive moment, in a decisive place by combining and mutually using the final results of all operations (battles) aimed at achieving the goal, as well as the ability to apply the conditions of a specific situation in the interests of timely deployment of comprehensively supported groups to conduct planned operations (battles).

Model development(calculations) and analysis of their results can have the following order: the general ratio of forces of the parties in the area of ​​​​the operation (battle) at the time of her the beginnings, as well as variants of plans for the actions of the enemy and friendly troops; a criterion for evaluating possible plans is selected; the expected results are calculated according to the selected criterion for all combinations of variants of their plans; the results are analyzed and the most appropriate plan for the operation (battle) is selected.

When determining each option actions of one and the other side, selected for evaluation, must be formulated: Where(in which direction, in which area, in which zone, strip and against which enemy objects), When(at what point, period) and How(in what way, method, technique, etc.) it is necessary to create an overwhelming superiority over the enemy. Changing the answer to at least one of these questions gives rise to a new version of the plan of action for this party.

The criterion for assessing the options of action of the parties in all their possible combinations can be the probability of defeating the enemy (completing the assigned task) or the balance of forces of the parties in the main direction at the decisive moment of the operation (battle). Translating this into the language of mathematics, we can say: in the main direction, at the decisive moment, one must be able (namely “able” - this is the art of a military leader, within the limits of the material capabilities of the troops) to create such a balance of forces in one’s favor, in which the assigned task would be completed with probability, for example, not less than 0.8. It should be emphasized that we are talking about a qualitative relationship between the forces of the parties, expressed in quantitative quantities. This probability of defeat serves as a criterion for selecting the most appropriate options for the design of the upcoming operation.

It is advisable to analyze the calculation results and select the optimal variant of the operation (battle) plan using game theory. It should be borne in mind that in this case such options are determined, using which the opposing parties do not risk losing more or winning less than is possible according to the chosen criterion in a given situation.

If the enemy is equal or stronger both in the composition of troops and in the level of military art, the choice of “guaranteed” plans can never ensure the achievement of victory. Therefore, in the proposed method of modeling an operation (combat) for analysis using game theory, it is necessary to select only those variants of the plans of the parties in which overwhelming superiority over the enemy is achieved at the decisive moment, in the decisive place of the battle (operation). Naturally, this is risky, but without this it is impossible to defeat a strong opponent. From them, you can choose the one that is relatively best according to the criterion that must be established by the commander (commander) developing the plan.

We will try to demonstrate the application of the proposed approach to creating mathematical models using two classical examples.

In the famous battle of Cannae (216 BC), the Carthaginian commander Hannibal, despite the double overall numerical superiority of the enemy, almost completely destroyed the Roman army. The total strength and losses of the parties were as follows:

This was no accidental victory. Even before the battle began, Hannibal set himself the goal not only of achieving success, but of completely destroying the Roman army. He skillfully brought his plan to life.

The Roman infantry was formed into a battle formation (phalanx), with at least 34 ranks in depth and about 1,700 men along the front. The cavalry was located on the flanks. Hannibal's troops were built in six columns, of which the middle two (totaling 20 thousand people) consisted of weak Spanish and recently recruited Gallic infantry. They were surrounded by two columns of 6 thousand experienced African veterans. On the flanks of the infantry there were cavalry columns: on the left - heavily armed cavalry (Gazdrubal's cuirassiers), on the right - light cavalry (mostly Numidian).

The further course of events was as follows. With the start of the battle, Gazdrubal's cavalry overthrew the Roman horsemen, part of their forces helped the Numidian cavalry put to flight the Roman horsemen on the left flank of the Roman infantry, and with the main forces rushed to the rear of the phalanx, forcing it to first turn back and then stop. In the center of the front, after a short battle, the Romans decisively attacked the Gauls and Spaniards, inflicting heavy losses on them and forcing the Carthaginian Center to retreat. The personal presence of Hannibal here kept the Gauls from breaking the front and fleeing. At this decisive moment, under the influence of a blow from the rear, the Roman phalanx stopped, which meant its death, only the outer ranks of the surrounded crowd of Roman legions could act with weapons, and the rear ones represented a target for flying stones, darts and arrows. The outcome of the battle was decided. What followed was a massacre.

Based on the actual course of events, the verbal model of the actions of the Carthaginian troops, i.e. Hannibal’s plan, can be formulated as follows: with small forces to hold back the first onslaught of the phalanx of Roman infantry in the center, sweep away the Roman cavalry on the flanks, completely encircle and stop the advance of the phalanx with a blow from the rear, thereby depriving it of offensive power, and, using its slowness and the poor training of the Roman infantry, completely defeat the enemy. The plan of the Roman commander Servilius: to direct the entire force of the infantry to the center of the battle formation of the Carthaginians, crush the enemy with a decisive attack, putting him to flight, and then one by one defeat the scattered units of the infantry and cavalry.

The essence of the current conflict situation and the entire calculation here boil down to resolving one question: who had more chances - Hannibal to hold back the onslaught of the Roman phalanx in the center until the moment when Gazdrubal's cavalry struck at it from the rear and stopped it, or Servilius , to crush the center of the Carthaginian battle formation, before stopping and rebuilding the phalanx for action in other directions? A mathematical description of the actions of the troops of the parties themselves is not required to resolve this issue.

Having analyzed, as they say, “in reverse” the final result of the battle from the standpoint of the essence of the art of war, we can say that at the decisive moment of the battle in the decisive direction (in the center), Hannibal was able to create (by striking the phalanx from the rear) an overwhelming (at least at least fourfold) superiority over the enemy and thereby prevented the crushing of the center of his infantry.

During the Great Patriotic War During the conduct of military operations in the Stalingrad direction, a situation arose similar to that discussed above, only with a different overall quantitative ratio of troops of the warring parties and a much greater scope of military operations. Judging by the actual course of events, the general plan of our troops was to hold the right bank of the Volga in the Stalingrad area with small forces, concentrate superior forces on the flanks of the Nazi group, encircle and destroy it with converging blows.

To substantiate this plan, in my opinion, it is enough to create a mathematical model that would solve one question: who has a better chance - our troops, to hold a bridgehead on the right bank of the Volga at least until the enemy is completely encircled, or the enemy, who needed to throw our defending troops into the Volga before turning our troops to meet our advancing troops? It would be inappropriate to develop a complex mathematical model of such large-scale military operations to justify this plan: it would not give more accurate, reliable results. Quite the contrary.

Of course, by analyzing individual examples, one cannot draw categorical conclusions. But some thoughts can be expressed.

First. Models that do not take into account the military skill of commanders will not fully reflect objective reality and will always give an unambiguous answer: the side that has numerical superiority and greater material capabilities will win. The use of such models will teach officers to win with numbers, not skill. In order to take into account the level of military art in mathematical models and develop appropriate coefficients, it is necessary to carefully analyze historical experience, as shown above in two examples.

Second. The main condition for the successful use of the proposed approach is the ability to identify the essence of conflict situations that arise during the preparation and conduct of military operations, and evaluate them from the point of view of the essence of the art of war.

Third. The shorter, clearer and clearer the plans of the parties' actions are formulated, the easier it is to identify the essence of the emerging conflict situation and identify the issue that requires calculations for its solution. The simpler the model, the closer it is to reality, the less distorted it reflects, and the less initial information it requires. Obviously, the mathematical apparatus for such models will also be simple (within the framework of probability theory and game theory).

Let us recall that the proposed approach applies only to models for justifying the intentions of decisions made. Mathematical models for research purposes, graphical display on the screen of decisions made on the current situation, and others are not considered here.

In conclusion, we note that another generally well-known approach to creating models (which can conventionally be called “dueling”) deserves attention, when the commander (commander) plays a “chess game” with a computer simulating the enemy. Of course, this path is difficult and time-consuming, but, in my opinion, promising from the point of view of increasing the efficiency of training officers in the art of war.

The mathematical model and the methodology of operational-tactical calculations are one and the same.

Military Thought.- 1987.- No. 7.- P. 33-41

Military encyclopedic dictionary. - M.: Voenizdat, 1986. - P. 89

Ibid.-S. 145.

Materials of the Plenum of the Central Committee of the CPSU, June 25-26, 1987 - M. Politizdat, 1987.-P. 12.

Soviet encyclopedic dictionary.- M.: Sov. encyclopedia, 1983.- P. 238

Military encyclopedic lexicon. - Part III. - St. Petersburg, 1839. - P. 454.

Marine Atlas-T. III.- Part 1.-MO USSR, 1958 -L. 1,

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The process of creating mathematical models of combat operations is labor-intensive, lengthy and requires the use of specialists of a sufficiently high level who have good training both in the subject area related to the object of modeling and in the field of applied mathematics, modern mathematical methods, programming, who know the capabilities and specifics of modern computing. technology. A distinctive feature of the mathematical models of combat operations currently being created is their complexity, due to the complexity of the objects being modeled. The need to build such models requires the development of a system of rules and approaches that can reduce the cost of model development and reduce the likelihood of errors that are difficult to eliminate later. An important component of such a system of rules are the rules that ensure the correct transition from a conceptual to a formalized description of the system in a particular mathematical language, which is achieved by choosing a specific mathematical scheme. A mathematical scheme is understood as a particular mathematical model for converting signals and information of a certain element of a system, defined within the framework of a specific mathematical apparatus and aimed at constructing a modeling algorithm for a given class of elements of a complex system.

In the interests of a reasonable choice of a mathematical scheme when constructing a model, it is advisable to classify it according to the purpose of modeling, method of implementation, type of internal structure, complexity of the modeling object, and method of representing time.

It should be noted that the choice of classification criteria is determined by the specific objectives of the study. The purpose of classification in this case is, on the one hand, a reasonable choice of a mathematical scheme for describing the process of combat operations and its representation in a model in the interests of obtaining reliable results, and on the other hand, identifying the features of the simulated process that must be taken into account.

The purpose of the simulation is to study the dynamics of the armed struggle process and evaluate the effectiveness of combat operations. Such indicators are understood as a numerical measure of the degree of completion of a combat mission, which can be quantitatively represented, for example, by the relative amount of prevented damage to defense facilities or damage inflicted on the enemy.

The method of implementation should consist in a formalized description of the logic of functioning of weapons models and military equipment(VVT) in accordance with their analogues in the actual process. It must be taken into account that modern weapons and military equipment are complex technical systems that solve a set of interrelated problems, which are also complex technical systems. When modeling such objects, it is advisable to preserve and reflect both the natural composition and structure, as well as the algorithms for the combat functioning of the model. Moreover, depending on the purposes of modeling, it may be necessary to vary these model parameters (composition, structure, algorithms) for different calculation options. This requirement determines the need to develop a model of a specific sample of weapons and military equipment as a composite model of its subsystems, represented by interconnected components.

Thus, according to the classification criterion, the type of internal structure, the model must be composite and multi-component, and according to the method of implementation, it must provide simulation modeling of combat operations.

Complexity of the modeling object. When developing components that determine the composition of models of weapons and military equipment, and combining models of weapons and military equipment into a single model of combat operations, it is necessary to take into account the characteristic scales of time averaging of quantities appearing in the components that differ by orders of magnitude.

The ultimate goal of modeling is to evaluate the effectiveness of combat operations. It is to calculate these indicators that a model is being developed that reproduces the process of combat operations, which we will conditionally call the main one. The characteristic time scale of all other processes included in it (primary processing of radar information, target tracking, missile guidance, etc.) is much less than the main one. Thus, it is advisable to divide all processes occurring in armed struggle into slow ones, the development forecast of which is of interest, and fast ones, the characteristics of which are not of interest, but their influence on the slow ones must be taken into account. In such cases, the characteristic time scale of averaging is chosen so as to be able to construct a model of the development of the main processes. As for fast processes, within the framework of the created model, an algorithm is needed that allows, at the moments of fast processes, to take into account their influence on slow ones.

There are two possible approaches to modeling the influence of fast processes on slow ones. The first is to develop a model of their development with a corresponding characteristic time scale of averaging, much smaller than that of the main processes. When calculating the development of a fast process in accordance with its model, the characteristics of slow processes do not change. The result of the calculation is a change in the characteristics of slow processes, which, from the point of view of slow time, occurs instantly. In order to be able to implement this method of calculating the influence of fast processes on slow ones, it is necessary to introduce the corresponding external quantities, identify and verify their models, which complicates all stages of the modeling technology.

The second approach consists in abandoning the description of the development of fast processes using models and considering their characteristics as random variables. To implement this method, it is necessary to have distribution functions of random variables that characterize the influence of fast processes on slow ones, as well as an algorithm that determines the moments of the onset of fast processes. Instead of calculating the development of fast processes, a random number is thrown out and, depending on the dropped value, in accordance with the known distribution functions of random variables, the value that the dependent indicators of slow processes will take is determined, thus taking into account the influence of fast processes on slow ones. As a result, the characteristics of slow processes also become random variables.

It should be noted that with the first method of modeling the influence of fast processes on slow ones, the fast process becomes slow, the main one, and its course is influenced by processes that are already fast in relation to it. This hierarchical nesting of fast processes into slow ones is one of the components of the quality of modeling the process of armed struggle, which classifies the model of combat operations as structurally complex.

Method of representing model time. In practice, three concepts of time are used: physical, model and processor. Physical time refers to the process being modeled, model time refers to the reproduction of physical time in the model, processor time refers to the execution time of the model on a computer. The ratio of physical and model time is specified by the coefficient K, which determines the range of physical time taken as a unit of model time.

Due to the discrete nature of the interaction of weapons and military equipment samples and their representation in the form of a computer model, it is advisable to set the model time by incrementing discrete time intervals. In this case, two options for its representation are possible: 1) discrete time is a sequence of real numbers equidistant from each other; 2) the sequence of time points is determined by significant events occurring in the simulated objects (event time). From the point of view of computing resources, the second option is more rational, since it allows you to activate an object and simulate its operation only when a certain event occurs, and in the interval between events, assume that the state of the objects remains unchanged.

One of the main tasks when developing a model is to fulfill the requirement of synchronization of all simulated objects in time, that is, the correct mapping of the order and temporal relationships between changes in the process of combat operations on the order of events in the model. With a continuous representation of time, it is believed that there is a single clock for all objects that shows the same time. The transfer of information between objects occurs instantly, and thus, by checking with a single clock, it is possible to establish the time sequence of all events that took place. If there are objects in the model with a discrete representation of time, in order to form a single model clock, it is necessary to combine many time samples of object models, order and define the values ​​of grid functions on the missing time samples. It is possible to synchronize object models with event time only explicitly, by transmitting a signal about the occurrence of an event. In this case, a control program-scheduler is needed for organizing the execution of events of various objects, which determines the required chronological order of event execution.

In a combat model, it is necessary to use event and discrete time together; this representation of time is called hybrid. When using it, the simulated objects acquire the property of changing the values ​​of some state indicators abruptly and almost instantly, that is, they become objects with hybrid behavior.

To summarize the above classification, we can conclude that the combat action model should be a composite, structurally complex, multi-component, dynamic, simulation model with hybrid behavior.

For a formalized description of such a model, it is advisable to use a mathematical scheme based on hybrid automata. In this case, samples of weapons and military equipment are represented as multicomponent active dynamic objects. Components are described by a set of state variables (external and internal), structure (single-level or hierarchical) and behavior (behavior map). Interaction between components is carried out by sending messages. To combine components into a model of an active dynamic object, the rules of composition of hybrid automata are used.

Let us introduce the following notation:

sÎRn - vector of object state variables, which is determined by a set of input influences on the object, influences of the external environment , internal (own) parameters of the object hkÎHk,;

A set of vector functions that determine the law of operation of an object in time (reflect its dynamic properties) and ensure the existence and uniqueness of the solution s(t);

S0 is the set of initial conditions, including all the initial conditions of the object components generated by the initialization function during operation;

A predicate that determines a change in the behavior of an object (selects the desired one from all specially selected states, checks the conditions that should accompany the event, and takes the value true when they are fulfilled) is specified by a set of Boolean functions;

An invariant that defines a certain property of an object that must be preserved over specified periods of time is specified by a set of Boolean functions;

- a set of real initialization functions that assign the value of the solution at the right end point of the current time interval to the value of the initial conditions at the left starting point at the new time interval: s()=init(s());

Hybrid time is specified by a sequence of time intervals of the form , - closed intervals.

The hybrid time elements Pre_gapi, Post_gapi are the “time gap” of the next step of the hybrid time tH=(t1, t2,…). At each clock cycle on segments of local continuous time, the hybrid system behaves like a classical dynamic system until the point t*, at which the predicate that determines the change in behavior becomes true. Point t* is the end point of the current and the beginning of the next interval. The interval contains two time slots in which state variables can change. The flow of hybrid time in the next clock cycle ti=(Pre_gapi,, Post_gapi) begins with the calculation of new initial conditions in the time slot Pre_gapi. After calculating the initial conditions, the predicate is checked at the left end of the new time interval. If the predicate evaluates to true, the transition is made immediately to the second time slot, otherwise a discrete sequence of actions corresponding to the current time step is performed. The Post_gapi time slot is designed to perform instant actions after the completion of long-term behavior at a given hybrid time step.

By hybrid system H we mean a mathematical object of the form

.

The modeling task is to find a sequence of solutions Ht=((s0(t),t, t0), (s1(t),t,t1),…), defining the trajectory of the hybrid system in the phase space of states. To find the sequence of solutions Ht, it is necessary to conduct an experiment or simulation on a model with given initial data. In other words, unlike analytical models, with the help of which a solution is obtained using known mathematical methods, in this case it is necessary to run a simulation model, and not a solution. This means that simulation models do not formulate their solution in the same way as is the case when using analytical models, but are a means and source of information for analyzing the behavior of real systems in specific conditions and making decisions regarding their effectiveness.

In the 2nd Central Research Institute of the Ministry of Defense of the Russian Federation (Tver), based on the representation of simulated objects in the form of hybrid automatic machines, a simulation modeling complex (IMK) “Seliger” was developed, designed to assess the effectiveness of groupings of forces and means of aerospace defense when repelling attacks from aerospace weapons. th attack (SVKN). The basis of the complex is a system of simulation models of objects, simulating algorithms for the combat functioning of real weapons and military equipment (anti-aircraft missile system, radar station, command post automation system (for radio engineering troops - radar company, battalion, brigade, for anti-aircraft missile forces - regiment, brigade etc.), combat aviation complex (fighter aircraft and aerospace attack weapons), electronic suppression equipment, non-strategic missile defense fire systems, etc.). Models of objects are presented in the form of active dynamic objects (ADO), which include components that make it possible to study the dynamics of various processes during their functioning.

For example, a radar station (radar) is represented by the following components (Fig. 1): antenna system (AS), radio transmitting device (RPrdU), radio receiving device (RPru), passive and active interference protection subsystem (PZPAP), primary information processing unit ( POI), secondary information processing unit (SOI), data transmission equipment (ADT), etc.

The composition of these components as part of the radar model makes it possible to adequately simulate the processes of receiving and transmitting signals, detecting echo signals and bearings, noise protection algorithms, measuring signal parameters, etc. As a result of the modeling, the main indicators are calculated that characterize the quality of the radar as a source of radar information (detection zone parameters, accuracy characteristics, resolution, performance, noise immunity, etc.), which allows you to evaluate the effectiveness of its operation when different conditions interference target environment.

Synchronization of all simulated objects in time, that is, the correct mapping of the order and temporal relationships between changes in the process of combat operations to the order of events in the model, is carried out by the object management program (Fig. 2). The functions of this program also include creating and deleting objects, organizing interaction between objects, and logging all events occurring in the model.

The use of an event log allows for a retrospective analysis of the dynamics of combat operations by any simulated object. This makes it possible to assess the degree of adequacy of object models both using limit point methods and by monitoring the correctness of modeling processes in the components of an object (that is, checking the adequacy by running from input to output), which increases the reliability and validity of the results obtained.

It should be noted that the multicomponent approach allows you to vary their composition (for example, to study the combat operation of air defense systems with different types ASCU) in the interests of synthesizing a structure that satisfies certain requirements. Moreover, due to the typing of the program representation of the components, without reprogramming the source code of the program.

The general advantage of this approach when building a model is the ability to quickly solve a number of research problems: assessing the impact of changes in the composition and structure of the control system (number of levels, control cycle, etc.) on the effectiveness of the combat operations of the group as a whole; assessment of the influence of various information support options on the potential combat capabilities of the samples and the group as a whole, research of forms and methods of combat use of the samples, etc.

The model of combat operations built on the basis of hybrid automata is a superposition of joint behavior of parallel and/or sequentially functioning and interacting multi-component ADOs, which are a composition of hybrid automata operating in hybrid time and interacting through message-based connections.

Literature

1. Sirota A.A. Computer modeling and efficiency assessment of complex systems. M.: Tekhnosphere, 2006.

2. Kolesov Yu.B., Senichenkov Yu.B. Systems modeling. Dynamic and hybrid systems. St. Petersburg: BHV-Petersburg, 2006.

To train the aerospace defense forces, a new material and technical base is needed, created on the basis of modern, maximally unified technical training tools, developed using modern technologies

Ensuring a high level of training of personnel - from the level of individual units to the highest levels of command - while simultaneously reducing material and financial costs is a very pressing issue for the training of troops (forces) and command and control bodies of the Aerospace Defense Forces.

The need to resolve this issue at present is due to the following factors:

• constant changes in the characteristics of the potential enemy’s means of armed warfare;
• the increasing dynamics of hostilities;
• participation of different types and types of air defense and missile defense forces and means in solving aerospace defense problems;
• the limited capabilities of the type of air targets used to create an airborne and jamming environment during tactical live-fire exercises at the training grounds of the Russian Defense Ministry;
• the increasing cost of conducting full-scale exercises and joint training of combat crews of various levels of command of the branches and branches of the military;
• limited capabilities of existing training facilities to integrate them into training complexes and training systems in the interests of comprehensive training of troops and command and control bodies of the aerospace defense region.

A possible approach to solving problematic issues related to the organization and conduct of combat and operational training activities may be the use of modern technologies for modeling armed confrontation, used in technical training facilities (TSO) for training troops (forces) and air defense command and control bodies.

Currently, a number of industrial organizations: the Center for Joint Technological Developments, the Research Institute "Tsentrprogramsistem", ZAO "CNTU "Dynamics", ZAO "NII TS "Sinvent", the Instrument Design Bureau, OJSC "Tulatochmash", etc., are working to create modern TSO for the Aerospace Defense Forces and the development of promising technologies for modeling military operations and training specialists of troops (forces) and command and control bodies of formations, aerospace defense associations.

However, their efforts are mainly focused on creating tactical-level technical training tools in the form of autonomous homogeneous simulators. These works do not imply the integration of simulators and training complexes into training systems for intraspecific and interspecific use, which sharply narrows the scope of their application in the training of military formations (MF) and command and control bodies solving aerospace defense problems.

In general, the type of TSO for the Aerospace Defense Forces may include:

• educational and training facilities;
• training complexes;
• training systems for intraspecific use;
• training systems for interspecific use.

It should be distinguished that an educational training facility (UTS) is a hardware and software complex that provides a full cycle of training combat crew numbers of one command level (unit) through automated theoretical training on the required types of training, the formation of initial skills and combat skills combat work (combat) through individual and autonomous training.

A training complex (TC) is a structural and organizational association of information-linked, geographically dispersed training equipment that provides the required level of practical readiness of crews at various levels of control, taking into account the level of automation of the combat process implemented in weapons and military equipment by conducting complex (two-level) training in the required conditions of combat use VVT.

The training system for intraspecific use (TS VP) is a structural and organizational unification of information-linked territorially dispersed technical complexes and training units in a tactical formation of troops, providing the required level of practical readiness and coordination of calculations of various levels of control by conducting joint (three-level) training of formations of military formations of the same type Sun.

The training system for interspecific use (TS MP) is a structural and organizational association of information-linked, territorially dispersed technical equipment and technical equipment for intraspecific use in an operational-tactical formation of troops, providing the required level of coherence among calculations at various levels of control by conducting joint training of formations of military formations of several types of armed forces.

In this regard, the created technical means of training combat crews of command posts and launchers of various levels of control of the Aerospace Defense Forces, taking into account the possible involvement of multi-service forces and means to prepare for solving aerospace defense tasks, should be considered at all levels of the proposed classification by purpose, depending on the specifics of combat and operational training activities .

The main problematic issues that remain in the development of training tools are:

• ensuring a high degree of adequacy of the simulation of the operation of equipment, systems and means of weapons and military equipment and controls;
• ensuring the required degree of adequacy of the simulated air and ground (if necessary, sea) situation with the real one;
• ensuring a unified simulated air and ground situation for all weapons and military equipment and military formations involved in training;
• coupling of geographically dispersed training facilities and training complexes into higher-level systems for conducting multi-level training of control bodies;
• synchronization in operating time of geographically dispersed simulators and training complexes for conducting various types of training as part of training systems;
• ensuring objectivity in assessing the level of professional preparedness of specialists, combat crews and command and control bodies based on the results of documenting their activities during the training process.

To train the Aerospace Defense Forces, a new material and technical base is needed, created on the basis of modern, maximally unified technical support systems, developed using modern technologies. The training of highly qualified specialists and control bodies, ready and capable at any time to qualitatively solve the tasks assigned to them in any environmental conditions, is practically impossible without systematic training with simulation of situations that may arise in a real combat situation, including non-standard (non-standard, emergency) situations .

Taking into account the domestic and foreign practice of developing TSOs, the following concept for their creation is proposed:

• firstly, this is the creation of a multi-level system of simulation and mathematical models of weapons and military equipment (WME) in the preparation of military forces (Fig. 1);

• secondly, it is the integration of the created simulation models of weapons and military equipment, airborne elements and training equipment into a single modeling environment in order to create and use a single virtual combat space when conducting combat and operational training activities (Fig. 2);

• thirdly, simulation models of weapons and military equipment and training facilities must interact with each other and with the modeling environment through the implementation of the IEEE-1516 distributed modeling standard, that is, using the HLA - High Level Architecture technology (Fig. 3).

The creation of modern technical training facilities will practically ensure the implementation of the LVC concept of troop training, which is based on the integrated use of three types of modeling: combat reality, virtual and constructive modeling. Moreover, each modeling segment actually determines the design features of the TSO and its scope of application (Fig. 4).

Thus, modeling of combat reality (Live Simulator, L-segment) involves the use of real military personnel and real systems when conducting tactical exercises (TC) at various levels. In the process of carrying out combat training activities, troops use real weapons in real conditions. The effects of interaction can be indicated by playing along with the opposite side using targets during live firing and flights of real aviation during firing training. This type of modeling is typical for East Kazakhstan region test sites.

Virtual simulation (Virtual Simulator, V-segment) involves the work of real people with simulated systems in an information modeling environment, that is, the use of various types and types of simulators during combat training activities aimed at individual training of trainees, training and coordination of combat crews, crews CP (PU) of various management levels (see Fig. 3). This type of modeling is applicable in places of permanent deployment when conducting various types of training.

Constructive Simulator (C-segment) includes simulated personnel, equipment, weapons and military formations. Real people control the simulation, in which simulated troops, equipment and weapons interact (Fig. 5). A similar modeling system should be used to conduct training activities in the preparation of control bodies (CO). This type of modeling is applicable when conducting computer command and staff training (CST) and command and staff exercises (CSE) of the OU starting from the tactical level.

The integrated use of the above types of modeling suggests the possibility of combining them into training systems for intraspecific and interspecific use. The proposed version of the vehicle for the interspecific use of air defense missiles (Aerospace Defense, Air Force, Navy Air Defense, Air Defense Forces of the Air Force) in the conditions of the ground is presented in Figure 6, where the air (background) situation is created by combining flights of real and simulated targets. Signals from simulated targets arrive at the input of air defense and radio-receiving means in the same way as signals from real targets, and create a general situation. At the same time, real aviation is working on ways to overcome air defenses and destroy defense targets through the use of aviation weapons. It should be noted that simulated targets can also be created on the basis of aviation simulators with three-dimensional visualization of the situation for pilots. Features of the architecture of the aerospace defense training ground, which implements the LVC concept of troop training, are presented in Figure 7.

It must be taken into account that the integration of training tools (simulators, training complexes and systems) into the UIMS will require solving key problems of a systemic nature, namely:

• methodological– development of new programs and training methods in conjunction with the creation of new generations of technical personnel and equipping the training material and technical base of troops with them;
• systems engineering– implementation of the transition to the modular principle of constructing TSO hardware and software on a qualitatively new information technology base;
• technological– creation of a domestic technological base for the development of new generation teaching aids for intraspecific and interspecific use.

Possible directions for solving the noted problems should be considered:

• use of promising element base and modern hardware and software when creating promising TSOs;
• the use of hardware and software built on the basis of certified software and hardware systems (STC), adapted for use as part of training systems for the Aerospace Defense Forces;
• the maximum possible unification of hardware and software included in the training systems for the Aerospace Defense Forces;
• interface of hardware and software that are part of the training systems of the Aerospace Defense Forces, based on high-level integration technologies;
• integration of previously developed and being developed simulators (training complexes) into a unified information modeling environment (UIMS) based on distributed modeling technology;
• use of EIMS for all means involved in conducting various types of training;
• integration of various modeling segments (V-segment, C-segment) to conduct complex and multi-level training of units, units and formations and training facilities according to a single plan and scenario;
• use of comprehensive information security systems to ensure the security of processing, storage and transmission of information.

In our opinion, the implementation of the noted areas will create a promising technological base for the creation of training systems for intraspecific and interspecific use and ensure:

• increasing the share of trained specialists for the Aerospace Defense Forces, despite the reduction in the total duration of service in the Armed Forces;
• intensive training of personnel of units and formations of the Aerospace Defense Forces based on testing scenarios of any complexity as conceived by the training director;
• comprehensive training of units and command and control bodies of military formations of the Aerospace Defense Forces to perform combat missions at a higher methodological and technical level;
• achieving maximum objectivity in monitoring the level of training of military personnel, units, formations and command and control bodies;
• improving the skills of commanders and command and control officials in decision-making and organizing interaction, and solving other problems;
• increasing the moral and psychological stability of personnel in conditions close to reality.

According to our estimates, the implementation of the LVC concept of training troops and command and control bodies proposed for use in the Aerospace Defense Forces will ensure a significant reduction in costs (7-12 times) for coordinating interspecific groupings of air defense forces and means in relation to the designation of the air enemy using real flight funds. The scientific potential for further development of the LVC concept has the VA East Kazakhstan region named after. G.K. Zhukov, and practical experience in its implementation in training troops in promising combat training centers - JSC NPO Russian Basic Information Technologies, which allows us to conclude that it is advisable to share the potential of these institutions (enterprises) when carrying out work to create promising combat training centers (CPC) of the Aerospace Defense Forces.

The process of creating mathematical models of combat operations is labor-intensive, lengthy and requires the use of specialists of a sufficiently high level who have good training both in the subject area related to the object of modeling and in the field of applied mathematics, modern mathematical methods, programming, who know the capabilities and specifics of modern computing. technology. A distinctive feature of the mathematical models of combat operations currently being created is their complexity, due to the complexity of the objects being modeled. The need to build such models requires the development of a system of rules and approaches that can reduce the cost of model development and reduce the likelihood of errors that are difficult to eliminate later. An important component of such a system of rules are the rules that ensure the correct transition from a conceptual to a formalized description of the system in a particular mathematical language, which is achieved by choosing a specific mathematical scheme. A mathematical scheme is understood as a particular mathematical model for converting signals and information of a certain element of a system, defined within the framework of a specific mathematical apparatus and aimed at constructing a modeling algorithm for a given class of elements of a complex system.

In the interests of a reasonable choice of a mathematical scheme when constructing a model, it is advisable to classify it according to the purpose of modeling, method of implementation, type of internal structure, complexity of the modeling object, and method of representing time.

It should be noted that the choice of classification criteria is determined by the specific objectives of the study. The purpose of classification in this case is, on the one hand, a reasonable choice of a mathematical scheme for describing the process of combat operations and its representation in a model in the interests of obtaining reliable results, and on the other hand, identifying the features of the simulated process that must be taken into account.

The purpose of the simulation is to study the dynamics of the armed struggle process and evaluate the effectiveness of combat operations. Such indicators are understood as a numerical measure of the degree of completion of a combat mission, which can be quantitatively represented, for example, by the relative amount of prevented damage to defense facilities or damage inflicted on the enemy.

The method of implementation should consist of a formalized description of the logic of functioning of weapons and military equipment (WME) in accordance with their analogues in the actual process. It must be taken into account that modern weapons and military equipment are complex technical systems that solve a set of interrelated problems, which are also complex technical systems. When modeling such objects, it is advisable to preserve and reflect both the natural composition and structure, as well as the algorithms for the combat functioning of the model. Moreover, depending on the purposes of modeling, it may be necessary to vary these model parameters (composition, structure, algorithms) for different calculation options. This requirement determines the need to develop a model of a specific sample of weapons and military equipment as a composite model of its subsystems, represented by interconnected components.

Thus, according to the classification criterion, the type of internal structure, the model must be composite and multi-component, and according to the method of implementation, it must provide simulation modeling of combat operations.

Complexity of the modeling object. When developing components that determine the composition of models of weapons and military equipment, and combining models of weapons and military equipment into a single model of combat operations, it is necessary to take into account the characteristic scales of time averaging of quantities appearing in the components that differ by orders of magnitude.

The ultimate goal of modeling is to evaluate the effectiveness of combat operations. It is to calculate these indicators that a model is being developed that reproduces the process of combat operations, which we will conditionally call the main one. The characteristic time scale of all other processes included in it (primary processing of radar information, target tracking, missile guidance, etc.) is much less than the main one. Thus, it is advisable to divide all processes occurring in armed struggle into slow ones, the development forecast of which is of interest, and fast ones, the characteristics of which are not of interest, but their influence on the slow ones must be taken into account. In such cases, the characteristic time scale of averaging is chosen so as to be able to construct a model of the development of the main processes. As for fast processes, within the framework of the created model, an algorithm is needed that allows, at the moments of fast processes, to take into account their influence on slow ones.

There are two possible approaches to modeling the influence of fast processes on slow ones. The first is to develop a model of their development with a corresponding characteristic time scale of averaging, much smaller than that of the main processes. When calculating the development of a fast process in accordance with its model, the characteristics of slow processes do not change. The result of the calculation is a change in the characteristics of slow processes, which, from the point of view of slow time, occurs instantly. In order to be able to implement this method of calculating the influence of fast processes on slow ones, it is necessary to introduce the corresponding external quantities, identify and verify their models, which complicates all stages of the modeling technology.

The second approach consists in abandoning the description of the development of fast processes using models and considering their characteristics as random variables. To implement this method, it is necessary to have distribution functions of random variables that characterize the influence of fast processes on slow ones, as well as an algorithm that determines the moments of the onset of fast processes. Instead of calculating the development of fast processes, a random number is thrown out and, depending on the dropped value, in accordance with the known distribution functions of random variables, the value that the dependent indicators of slow processes will take is determined, thus taking into account the influence of fast processes on slow ones. As a result, the characteristics of slow processes also become random variables.

It should be noted that with the first method of modeling the influence of fast processes on slow ones, the fast process becomes slow, the main one, and its course is influenced by processes that are already fast in relation to it. This hierarchical nesting of fast processes into slow ones is one of the components of the quality of modeling the process of armed struggle, which classifies the model of combat operations as structurally complex.

Method of representing model time. In practice, three concepts of time are used: physical, model and processor. Physical time refers to the process being modeled, model time refers to the reproduction of physical time in the model, processor time refers to the execution time of the model on a computer. The ratio of physical and model time is specified by the coefficient K, which determines the range of physical time taken as a unit of model time.

Due to the discrete nature of the interaction of weapons and military equipment samples and their representation in the form of a computer model, it is advisable to set the model time by incrementing discrete time intervals. In this case, two options for its representation are possible: 1) discrete time is a sequence of real numbers equidistant from each other; 2) the sequence of time points is determined by significant events occurring in the simulated objects (event time). From the point of view of computing resources, the second option is more rational, since it allows you to activate an object and simulate its operation only when a certain event occurs, and in the interval between events, assume that the state of the objects remains unchanged.

One of the main tasks when developing a model is to fulfill the requirement of synchronization of all simulated objects in time, that is, the correct mapping of the order and temporal relationships between changes in the process of combat operations on the order of events in the model. With a continuous representation of time, it is believed that there is a single clock for all objects that shows the same time. The transfer of information between objects occurs instantly, and thus, by checking with a single clock, it is possible to establish the time sequence of all events that took place. If there are objects in the model with a discrete representation of time, in order to form a single model clock, it is necessary to combine many time samples of object models, order and define the values ​​of grid functions on the missing time samples. It is possible to synchronize object models with event time only explicitly, by transmitting a signal about the occurrence of an event. In this case, a control program-scheduler is needed for organizing the execution of events of various objects, which determines the required chronological order of event execution.

In a combat model, it is necessary to use event and discrete time together; this representation of time is called hybrid. When using it, the simulated objects acquire the property of changing the values ​​of some state indicators abruptly and almost instantly, that is, they become objects with hybrid behavior.

To summarize the above classification, we can conclude that the combat action model should be a composite, structurally complex, multi-component, dynamic, simulation model with hybrid behavior.

For a formalized description of such a model, it is advisable to use a mathematical scheme based on hybrid automata. In this case, samples of weapons and military equipment are represented as multicomponent active dynamic objects. Components are described by a set of state variables (external and internal), structure (single-level or hierarchical) and behavior (behavior map). Interaction between components is carried out by sending messages. To combine components into a model of an active dynamic object, the rules of composition of hybrid automata are used.

Let us introduce the following notation:

sÎRn - vector of object state variables, which is determined by a set of input influences on the object, influences of the external environment , internal (own) parameters of the object hkÎHk,;

A set of vector functions that determine the law of operation of an object in time (reflect its dynamic properties) and ensure the existence and uniqueness of the solution s(t);

S0 is the set of initial conditions, including all the initial conditions of the object components generated by the initialization function during operation;

A predicate that determines a change in the behavior of an object (selects the desired one from all specially selected states, checks the conditions that should accompany the event, and takes the value true when they are fulfilled) is specified by a set of Boolean functions;

An invariant that defines a certain property of an object that must be preserved over specified periods of time is specified by a set of Boolean functions;

- a set of real initialization functions that assign the value of the solution at the right end point of the current time interval to the value of the initial conditions at the left starting point at the new time interval: s()=init(s());

Hybrid time is specified by a sequence of time intervals of the form , - closed intervals.

The hybrid time elements Pre_gapi, Post_gapi are the “time gap” of the next step of the hybrid time tH=(t1, t2,…). At each clock cycle on segments of local continuous time, the hybrid system behaves like a classical dynamic system until the point t*, at which the predicate that determines the change in behavior becomes true. Point t* is the end point of the current and the beginning of the next interval. The interval contains two time slots in which state variables can change. The flow of hybrid time in the next clock cycle ti=(Pre_gapi,, Post_gapi) begins with the calculation of new initial conditions in the time slot Pre_gapi. After calculating the initial conditions, the predicate is checked at the left end of the new time interval. If the predicate evaluates to true, the transition is made immediately to the second time slot, otherwise a discrete sequence of actions corresponding to the current time step is performed. The Post_gapi time slot is designed to perform instant actions after the completion of long-term behavior at a given hybrid time step.

By hybrid system H we mean a mathematical object of the form

.

The modeling task is to find a sequence of solutions Ht=((s0(t),t, t0), (s1(t),t,t1),…), defining the trajectory of the hybrid system in the phase space of states. To find the sequence of solutions Ht, it is necessary to conduct an experiment or simulation on a model with given initial data. In other words, unlike analytical models, with the help of which a solution is obtained using known mathematical methods, in this case it is necessary to run a simulation model, and not a solution. This means that simulation models do not formulate their solution in the same way as is the case when using analytical models, but are a means and source of information for analyzing the behavior of real systems in specific conditions and making decisions regarding their effectiveness.

In the 2nd Central Research Institute of the Ministry of Defense of the Russian Federation (Tver), based on the representation of simulated objects in the form of hybrid automatic machines, a simulation modeling complex (IMK) “Seliger” was developed, designed to assess the effectiveness of groupings of forces and means of aerospace defense when repelling attacks from aerospace weapons. th attack (SVKN). The basis of the complex is a system of simulation models of objects, simulating algorithms for the combat functioning of real weapons and military equipment (anti-aircraft missile system, radar station, command post automation system (for radio engineering troops - radar company, battalion, brigade, for anti-aircraft missile forces - regiment, brigade etc.), combat aviation complex (fighter aircraft and aerospace attack weapons), electronic suppression equipment, non-strategic missile defense fire systems, etc.). Models of objects are presented in the form of active dynamic objects (ADO), which include components that make it possible to study the dynamics of various processes during their functioning.

For example, a radar station (radar) is represented by the following components (Fig. 1): antenna system (AS), radio transmitting device (RPrdU), radio receiving device (RPru), passive and active interference protection subsystem (PZPAP), primary information processing unit ( POI), secondary information processing unit (SOI), data transmission equipment (ADT), etc.

The composition of these components as part of the radar model makes it possible to adequately simulate the processes of receiving and transmitting signals, detecting echo signals and bearings, noise protection algorithms, measuring signal parameters, etc. As a result of the modeling, the main indicators are calculated that characterize the quality of the radar as a source of radar information (detection zone parameters, accuracy characteristics, resolution, performance, noise immunity, etc.), which makes it possible to evaluate the effectiveness of its operation under various conditions of the target noise environment.

Synchronization of all simulated objects in time, that is, the correct mapping of the order and temporal relationships between changes in the process of combat operations to the order of events in the model, is carried out by the object management program (Fig. 2). The functions of this program also include creating and deleting objects, organizing interaction between objects, and logging all events occurring in the model.

The use of an event log allows for a retrospective analysis of the dynamics of combat operations by any simulated object. This makes it possible to assess the degree of adequacy of object models both using limit point methods and by monitoring the correctness of modeling processes in the components of an object (that is, checking the adequacy by running from input to output), which increases the reliability and validity of the results obtained.

It should be noted that the multicomponent approach allows you to vary their composition (for example, to study the combat operation of air defense systems with different types of automated control systems) in the interests of synthesizing a structure that satisfies certain requirements. Moreover, due to the typing of the program representation of the components, without reprogramming the source code of the program.

The general advantage of this approach when building a model is the ability to quickly solve a number of research problems: assessing the impact of changes in the composition and structure of the control system (number of levels, control cycle, etc.) on the effectiveness of the combat operations of the group as a whole; assessment of the influence of various information support options on the potential combat capabilities of the samples and the group as a whole, research of forms and methods of combat use of the samples, etc.

The model of combat operations built on the basis of hybrid automata is a superposition of joint behavior of parallel and/or sequentially functioning and interacting multi-component ADOs, which are a composition of hybrid automata operating in hybrid time and interacting through message-based connections.

Literature

1. Sirota A.A. Computer modeling and efficiency assessment of complex systems. M.: Tekhnosphere, 2006.

2. Kolesov Yu.B., Senichenkov Yu.B. Systems modeling. Dynamic and hybrid systems. St. Petersburg: BHV-Petersburg, 2006.