Methodology of qualitative analysis of large military systems.

One of the results of studies carried out by the 27th Central Research Institute of the RF Defense Ministry over the last 15 years is the development of a new class of highly aggregated mathematical models (AMM) to appraise combat capabilities of force groupings in operations. The set of methods used for creating them is outside the bounds of conventional methods used in studying operations and it uses techniques of such mathematical disciplines as stability and bifurcation theory and catastrophe theory.

Mathematical models of this class are used in the initial phase of operation planning--to develop the concepts of plans for the employment of armed forces and to determine numerical and effective combat strength of force groupings in theaters, general characteristics of their operational-strategic disposition and the scope of tasks of force groupings in operations. Since the phase of general (strategic) planning of the employment of armed forces is characterized by the greatest uncertainty of input data, mathematical models supporting this phase should describe only fundamental, qualitative properties of operations in hand rather than their detailed characteristics.

Such mathematical models are based on qualitative analysis of big military systems (BMS) which imply systems comprised of two subsystems or opposing force groupings in a strategic sector (including systems that control them).

In terms of dynamic systems theory, qualitative analysis involves first of all the examination of the dynamic and structural stability of a system by analyzing its phase portrait and its bifurcations under the action of controlling parameters. It implies operating with the phase portrait of the system as a whole rather than with the final aggregate of its phase trajectories. For this reason this kind of analysis offers the possibilities for the direct approach, i.e., conventional (multivariant) modeling of phase trajectories are very limited.

Qualitative analysis implies determination of the critical (bifurcational) set within the scope of controlling parameters termed as a separatrix and description of phased transition of the system from one stable condition to another. The separatrix divides the parametric space into areas with qualitatively different types of the system's dynamic behavior.

This highlights the role of qualitative analysis of BMS as a tool of general planning for the employment of armed forces: changing the effective combat and numerical strength of force groupings in theaters, the scope of their tasks in operations, their operational-strategic disposition (the necessary density of troops) at specified (or varying) characteristics of the control system leads to the shifting of external control parameters from one area of the parametrical space to another. Varying these data and having in front of himself an image of the separatrix (or its section), the operator can interactively adjust decisions being taken in such a way as to bring control parameters into an area with desirable dynamic characteristics of functioning of the system in hand.

It follows that the vital element of the qualitative analysis method is parameterization of dynamic systems under investigation. It is parameterization that distinguishes aggregated models of the class being investigated from models of "pointwise" estimation because it alone can lend models the nature of recommendations. However, parameterization comes at a cost, that is to say, we have to pay for switching over to families of functions with nonlinearity of models.

The class of gradient dynamic systems bears a direct relation to solving the problems of general planning for the employment of armed forces. Their phase portraits are special in that they have critical points of the so-called potential function specified above the phase coordinates. Methods of entering potential BMS functions constitute the core of the methodology of qualitative analysis of the latter. A potential function is entered into the coordinates of the aggregated variable of state and then external control parameters (along with the number and quality of the sides' weaponry conventionally accounted for in models of operations) are used to enter into this function an aggregated parameter of command and control which depends on decisions being taken in the strategic control echelon. The solving of such problems consists in determining the operation's objective, the resources allotted for achieving it and general characteristics of the force grouping's operational-strategic disposition. Furthermore, this parameter contains characteristics of the control system and supporting systems--effectiveness of reconnaissance, the number of command centers, their survivability, the number of types of communication facilities and reliability of their functioning, the extent of automation and capacity of the appropriate element of the automated command and control system. (1)

Families of potential functions for the appraisal of combat potentialities of force groupings in operations contain up to four mathematical controlling parameters. A collection of methods that make it possible to express these parameters in terms of physical control parameters (numerical and effective combat strength of force groupings in theaters and the scope of their tasks in operations) forms the second main component of the qualitative analysis methodology. To develop these methods is the greatest problem. To solve it we use the principle of equivalency of description of stable states of equilibrium of BMS on macro- and micro-levels. Corresponding to stable states of equilibrium of BMS on macro-levels are minimums of the potential function, and minimums of some or other thermodynamic potential, on the micro-level. As a result, it is possible to obtain connection between the mathematical controlling parameters and the physical parameters through coordinating the appropriate models of the above levels.

Finally, the third component of the methodology of qualitative analysis of BMS is comprised of mathematical methods of catastrophe theory that make it possible, on the basis of a derived family of potential functions to construct the sought for critical set (separatrix) in the space of controlling parameters and describe the diversity of qualitative changes occurring in a system when we adjust controlling parameters.

When analyzing systems determined by means of probability distributions over the space of variables of state, the study of the phase portrait topology and its bifurcations is substituted by the study of topology of probability distributions and its bifurcations under the action of controlling parameters. We introduce with regard to these systems a family of such functions which fully describe the topology of appropriate probability distributions (they concentrate around minimums of the potential function). Thus, the catastrophe theory methodology can be successfully used also for constructing probability AMM.

Interest in further development of quality theory of dynamic systems among military people in other countries came into evidence in the mid-1970s. This interest at first showed in bankrolling theoretical studies. In the 1980s, these studies focussed on analysis of the behavior of military systems. But publications related to them contained scarce information of methodological nature and were mainly intended to illustrate the possibilities of using catastrophe theory tools in applied military studies.

Our initial research into creating aggregated mathematical models to appraise combat capabilities of force groupings in operations also dates from that time. The second half of the 1980s saw the introduction of new basic terms such as "efficiency potential," "possibility potential," "potential function of BMS," "critical set," etc. The results of that period of studies, especially those relating to nonlinear aggregating, were largely heuristic and helped to complete in 1990 the development of a system design and an AMM model encompassing all forms of strategic actions of armed forces. The follow-up studies focussed on strict mathematical formalization so as to rule out elements of opportunism in the use of catastrophe theory techniques.

Theoretical research and the development of software were at their height in 1991-1995. It is safe to assume that the work done at that time had qualitative analysis of BMS emerge as a new independent area of military research with its own concepts and terms and with its own field of application for the benefit of strategic element of armed forces control. On the practical side of the studies in that period was the creation of an AMM complex that made possible operational-strategic computations in the initial phase of planning for the employment of armed forces without having to resort to traditional operation modeling techniques which calls for inputs of information about operation scenarios of the sides that is not typical of the level of problems addressed by the General Staff in the initial phase of planning. The first Candidate of Science dissertation using elements of the new terms and methods was defended in 1992.

Further studies followed several directions in recent years:

* the transfer of methods of qualitative analysis of BMS to macrosystems of a different nature, including macrosystems with a homeostatic type of behavior; (2)

* the transfer of methods of qualitative analysis of BMS to smaller size systems--up to operational level force groupings; (3)

* the development of methods of BMS synthesis. (4)

It is reasonable that methods of qualitative analysis of BMS have gone through their formative phase and entered a phase of intensive development.

We would like to note in conclusion that the results obtained in the field of qualitative analysis of BMS can be effectively used, in addition to strategic planning of the employment of armed forces, in solving other important practical problems of force development and protection of national security.

NOTES:

1. Kh.I. Saifetdinov, N.A. Morozov, "K otsenke boevykh vozmoznostei gruppirovok voisk (sil) s uchetom faktora upravleniya," Voennaia mysl', No. 4, 1995; N.A. Morozov, Teoreticheskie osnovy kachestvennogo analiza bolshikh voennykh sistem: Monografiya, 27 TsNII MO RF, Moscow, 2003.

2. N.A. Morozov, "Upravlenie, izmerenie i ustoichivost sostoyanii v slozhnykh systemakh, vzaimodeistvuyushchikh s aktivnoi vneshnei sredoi," Informatizatsiya i svyaz, No. 2, 2000; N.A. Morozov, "Ob otsenke vozmozhnosti dostizheniya tselei upravleniya v makrosistemakh, vzaimodeystvuyushchikh s aktivnoi vneshnei sredoi," Nauchno-tekhnicheskoe prilozheniye k zhurnalu "Vooruzhenie, politika, konversiya", No. 3, 2002.

3. N.A. Morozov, V.V. Bakov, "K metodike parametrizatsii modeli dlya otsenki boevykh vozmozhnostei gruppirovok voisk (sil) v operatsiyakh," Nauchno-tekhnicheskii sbornik MO RF, No. 1, 2003.

4. N.A. Morozov, A.N. Kitnik, "Metodika optimizatsii struktury potentsiala gruppirovki na osnove modeli kriticheskogo mnozhestva," Nauchno-tekhnicheskii sbornik MO RF, No. 2, 2001.

Col. N.A. MOROZOV (Ret.)

Senior researcher, the 27th Central Scientific Research Institute of the RF Defense Ministry

Doctor of Technical Sciences