Information-and-method coordination of military operations models.

One of the main tools of logical analysis possessing a considerable intellectual content and more or less fully reflecting the military subject area are mathematical models of military operations of different scales. Repeated modeling of operations in accordance with different scenarios enables assigned personnel to make a comparative evaluation of variants of decisions and plans of employment of forces and fires and select the most rational of them.

To achieve unity of the command and control system with regard to the levels of hierarchy and subsystems, mathematical models of military operations should fit the requirement of information-and-method coordination. Thus, in modeling in the interests of validating decisions and planning military operations the results of modeling in various echelons should be coordinated with regard to time and space even if their levels of generalization should prove different. In other words, a decision of the upper echelon validated with the aid of modeling and sent as a directive to the lower echelon should be backed by the results of a more detailed subsequent modeling in the lower echelon. If it is planned on one hierarchical level of command and control to employ more than one combat arm, the results of modeling should be coordinated with the "output data" obtained in planning combat operations by separate combat arms. In controlling troops (forces) in local wars and armed conflicts, when getting a trouble stop under c ontrol is achieved via combat operations of, as a rule, tactical scale, it is unwise to use models of an army (still less frontal) operation in the work of staffs. There should be other sufficiently generalized models, but the results of modeling should be coordinated with the output data of detailed models used in tactical-echelon staffs.

From the above it is advisable in a general case to bring into three interconnected groups the requirements of information-and-method matching of models in accordance with the levels of command and control hierarchy and the types of processes being modeled: first--coordination of operational-tactical information (OTI), including initial information for modeling; second--coordination of the employed mathematical methods, calculation methods and algorithms; third--coordination of the criteria of calculated output indices of models.

The above requirements contradict the need for correspondence between the degree of detailing the description of processes being modeled and the hierarchical level of the control body that uses the model. The contradiction is especially acute in control bodies of the top echelon and consists in a contradiction between the high level of aggregation (generalization, enlargement) of operational-tactical information and the need for an appropriate reproduction in the model of combat processes taking account of all the tactical factors having substantial impacts on the course and outcome of combat.

This contradiction can be resolved on the basis of methods of aggregation and decomposition of models. The task of aggregation of a model in general form consists of the following: having a mathematical model of the process to obtain as a consequence of it (precise or approximate) the so-called aggregated model which forms links not between the input variables and controlling effects, but between some of their functions or functionals. (1) The number of these values should be smaller than the number of input values, and links between them should be simpler in some sense.

Let us consider fundamental approaches to achieving information-method coordination of models.

Coordination of operational-tactical information. It is advisable, in tackling this problem, to carry out aggregation and decomposition of operational-tactical information using generalized semantic classes of information. We can accept as OTI classes the following:

1--effective combat strength of the friendly force grouping;

2--effective combat strength of the enemy force grouping;

3--battle order of the friendly troops;

4--battle order of the enemy;

5--weapon resources of the friendly troops;

6--weapon resources of the enemy;

7--terrain;

8--engineer preparation of the terrain;

9--command and control of troops;

10--logistic and technical support and so on.

In this case, the level of OIT aggregation can be characterized by the degree of detailing in each class determined from corresponding graduated scales. The essence of this approach can be represented in the form of matrix D, which we will call a matrix of detailing the OTI. The columns of the matrix correspond to the classes of information and its rows, to the degrees of information detailing.

Elements {[d.sub.ij]} of matrix D are the levels of detailing used in the OTI model on the class basis. For example, for the class "effective combat strength of the friendly force grouping" (i=1) the matrix elements will be [d.sub.11]--divisions, [d.sub.12]-- regiments (brigades), [d.sub.13]--battalions, etc.; for the class "battle order of the friendly troops" (i=3): [d.sub.31]--boundaries between divisions, [d.sub.32]--boundaries between regiments, [d.sub.33]--boundaries between battalions, etc.

Thus, the level of aggregation of OTI corresponding to the hierarchical level of the command and control organ can be reflected in the matrix (1) in the form of a boundary based on the collection of its elements (the solid line).

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At the same time the requisite level of information aggregation should be lower than that of OTI aggregation of the command and control organ under review (broken line) in order to be appropriately reproduced in the model of the combat operation process from the point of view of taking into account the essential tactical factors. Therefore, the contradiction formulated above can be represented in the matrix in the form of a zone of disparity between the existing and requisite levels of aggregation.

This contradiction can be resolved through: automatic detailing of the input OTI in model to achieve the requisite level based on information about the establishment of units and subunits and tactical standards characteristic of the opposing sides; the construction of a general algorithm controlling the process of modeling, which automatically adapts itself in accordance with prevailing situations, on the basis of tactical methods of conducting combat operations characteristic of the sides (in the "command and control of troops" OTI class).

Coordination of mathematical methods, computing methods and algorithms. The solving of this problem can be based on methods of decomposing and aggregating the description of the process of military operations, in particular, on the stratification method consisting in the construction of a general model in the form of a structured aggregate of coordinated models of processes that differ from each other in the extent of abstraction. (2) In other words, a model constructed on the basis of such an approach should reproduce the process of combat operations phase by phase in combination with more detailed methods of reproduction of the sides' impacts upon each other and taking into account all significant factors. It is possible to consider as a variant a three-level pattern of reproduction in the model of combat operation processes.

On the first level we model command and control of elements of combined units battle orders and construct the process of combat operations as a whole in the form of a sequence of phases. * The sequence and conditions under which the phases begin are determined at this level on the basis of detailed input data and the results of completion of the previous phases.

In the second phase we reproduce the phases of combat operations. Each of them is represented as a sequence of the sides' impacts upon each other with a certain time step called a modeling step. For example, the airstrike phase incorporates a sequence of such impacts: an airstrike at air defense assets, a response strike by the air defense assets at airplanes and helicopters, an airstrike at ground-based military targets. Based on corresponding standards we model: command and control of subunits (building up of combat efforts, target allocation and so on), combat, logistic and technical support. We also verify the conditions of completion of the phase as a whole or the cessation of some or other type of impact (once the weapons resource is up).

In the third phase we reproduce the methods by which the sides impact on each other within the scope of the modeling step. The method of impact of some or other type is described by analytical relationships that take into account all essential tactical factors and enabling computation of the most probable or averaged results of impacts.

An important element of the generalized model is a unit aggregating the results of modeling of combat operations so as to reach the level of effectiveness indices conforming to the problems being solved by staffs. The functional content of this unit is intended for achieving a correlation between the models' criteria and computed output indices.

Output indices in models of large-scale operations used in the work of corresponding staffs are indices of the course and the outcome of operations formed directly during modeling (depth of advance or penetration, losses and casualties, changes in relative strengths). They measure up to the problems tackled by the staff of large strategic formations and are sufficient to formulate concepts and plans of operations both in advance and right before holding them. Similar indices of the course and the outcome of combined-arms combats formed in tactical-scale models are used in the work of staffs of combined units (separate units) and correspond to their chief missions.

For their part, higher-echelon staffs tackle general problems based on the use of aggregated indices reflecting the forecast extents of achieving the objectives set to armed forces in local wars or local conflicts generally or in their separate phases. The objectives of employing armed forces in the given case can be expressed in definite combat missions: repulsing the enemy aggression and inflicting on it a damage making sure that it decides against further active actions; freeing territories captured by enemy armed elements; blocking enemy armed elements in a certain area to compel them to talks, and so on. One index of the result of combat operations is the degree (S) of the fulfilment of the combat mission. Considering the big scale of tasks tackled by staffs of top command and control echelons, we can consider as the most important the question of whether a combat mission was or was not fulfilled, ignoring intermediate variants. Therefore, S can be represented in the binary ("yes--no") variant which rule s out its ambivalent interpretation in the staffs and this at the same time simplifies the construction of aggregation of modeling results algorithms.

Thus, in a general form the characteristic of the result of combat operations R can be represented as a Boolean (binary) function

R = S([x.sub.1], [x.sub.2], ..., [x.sub.n]).

The function's arguments are logical variables, which result from comparing the indices of output data of the outcome of combat operations [r.sub.1], [r.sub.2], ..., [r.sub.n] (depth of advance, rate of advance, duration of combat, losses and casualties, etc.), formed in the course of modeling with corresponding step values of [[eta].sub.1], [[eta].sub.2], ..., [[eta].sub.n], i.e.

[x.sub.j] = {1, if [r.sub.j] [greater than or equal to] [[eta].sub.j] ([r.sub.j] [less than or equal to] [[eta].sub.j]) 0. (2)

The choice of inequality signs depends on the type of characteristic of outcome of the combat and its effect on the combat mission. It is advisable to represent the S function as a step function:

S([x.sub.1], [x.sub.2], ..., [x.sub.n]) = Sgn([summation over (N/j=1)][[epsilon].sub.j][x.sub.j] - [alpha]), (3)

where [[epsilon].sub.j] is the weight coefficient of the jth output characteristic of the outcome of the combat ([[epsilon].sub.j] [member of] [0, 1]);

[alpha] is the general threshold of fulfilling the combat mission ([alpha] > 0);

Sgn(A) = {1, if A [greater than or equal to] 0

0, if A < 0.

Thus, a formalized description of the combat mission uses values of the general threshold of its fulfilment [alpha] and three vectors: E = {[[[epsilon].sub.j]}, H = {[[eta].sub.j]}, [GAMMA] = {[[gamma].sub.j]}. Vector E is coefficients characterizing the substantiality of each output characteristic of outcome of the combat for the combat mission under consideration. A special case is the so-called "binary" formalization of the combat mission where values of the components of vector E are equal to 1, for the substantial output indices of outcome of the combat in the given combat mission, and 0, for the insubstantial output indices. Vector H contains threshold values of corresponding threshold indices of the combat's outcome representing (for the combat mission under consideration) "at the top" and "at the bottom." Vector [GAMMA] has values of its components equal to 1 in (2) with the inequality sign of the "[greater than or equal to]" type, and 0 with the inequality sign of the "[less than or equal to]" type.

Considering the suggested principle of aggregating output indices of the models, activities of staffs (from the mathematical point of view) can be represented as the solving of inverse tasks, i.e., tasks involving the finding of rational variants of achieving the objectives of military operations formulated in the form of combat missions. The assignment of such inverse tasks can be expressed in the following general form.

Let us write the multidimensional variable U = {[u.sub.1], [u.sub.2], ..., [u.sub.p]} of an aggregate of OTI values according to its classes p that appear in the columns of the detailing matrix D (1). Thus, it is required to find the value of the variable U, that minimizes a certain [PHI](U) goal function under a certain limitation on the values of the U components provided the combat mission is fulfilled (3), i.e., with R = 1. In this case the model of combat operations can be represented as a certain mathematical operator S(U) converting the value of the multidimensional variable U into the value of index R of fulfilling the combat mission.

In terms accepted here, the goal function reflects not the extent of reaching the goal of employing armed forces (fulfilment of the combat mission), but the extent of rationality of reaching the goal which is more often than not linked to minimization of forces, resources or time.

Thus, the solving of the inverse task formulated above would require the creation of a special program shell covering the model of combat operations and a number of other computed components. The most promising course of action in this respect is to use contemporary intelligent technologies, which makes it possible to attain a new qualitative level in developing sets of models and tasks, to wit, to create modeling systems intended for solving in staffs all main questions of planning the employment of RF Armed Forces.

* A phase implies a limited duration period of combat operations with certain conditions of its start and completion and characterized by methods determined for the entire period of the sides' impacts upon each other (for example, such phases as an air strike, preparation fire for the assault, combat for a defense position) or a certain manner of operation used by one of the sides (regrouping, committing reserves to battle).

NOTES:

(1.) See: G.I. Savin, Sistemnoye mnodelirovaniye slozhnykh protsessov. FAZIS, Moscow, 2000.

(2.) See: A.A. Pervozvanskiy, V.G. Gaytsgori, Dekompozitsiya, aggregirovaniye i priblizhennaya optimizatsiya, Nauka Publishers, Moscow, 1979.