The paper is dedicated to the possibility of using interaction model, based on idea of troops efforts coordination, which considers the interests not only of control subsystems (command center), but also the interests of active subsystems (combat elements), for their effectiveness estimation and optimal air defense system structure choosing. To achieve the interaction process harmonization the study of control subsystems stimulating impacts is required to compensate for the loss of active elements. The additional (synergistic) effect received by the system and elements in combined interactions is studied, as well as the loss of each element while general task performing. It is shown that the implementation of coordinated interactions in the system is possible only if the additional (synergistic) effect of all its elements exceeds their losses, and if the additional (synergistic) effect is less than the losses, the interaction inside the system with certain parameters is not effective, so its elements must carry out their missions separately from each other.The theoretical basis for solving problems of coordinated interaction is the theory of active systems and set theory.
In modern warfare, a very important role is
given to the fight against the enemy aircraft, the
task of which is entrusted to the air defense system
(AD System). The main task of the air defense
system is the destruction of enemy aircraft attack,
gaining and maintaining air superiority,
protection from air strikes of groups of troops
(forces), arsenals, bases, warehouses, airfields,
naval bases, industrial areas, administrative and
political centers, etc. [
Therefore, special attention is paid to the
organization of interaction between the Air
Defense Aircraft (AD Aircraft) and the Air
Defense Artillery (ADA) in order to make the
most complete and effective use of their combat
capabilities, as well as ensuring mutual security of
their troops (forces) in performing tasks [
Interaction is a managerial activity that is able
to create a cohesive and invincible force from a
handful of disparate parties that is self-learning
and continuously improving [
Interaction is one of the basic principles of
martial arts. It reflects the objective pattern of
mutual influence of all troops and forces involved
in the operation [
The problem of the interaction organizing
between the AD Aircraft and the ADA is very
sophisticated, as the nature of hostilities and
methods of combat use of troops are
interdependent. In addition, the effectiveness of
AD combat operations depends on the scale and
nature of the enemy's air defenses, the operational
construction of covered troops, combat
composition and combat capabilities of
interacting forces and means, meteorological
conditions, time of day and so on. All of this must
be taken into account during the organization and
implementation of interaction [
Therefore, it is necessary to integrate the elements of the air defense system, taking into account the consistency of their interests. This question can be assessed by using the synergetic theory of systems analysis.
The integration of AD aircraft with GBAD in
one zone, according to the synergetic theory, has
an additional systemic effect - emergence [
The task of synthesis of the interaction process is to choose individual or a set of its components from the standpoint of the criterion of efficiency of the active system, namely: the target functions of different levels elements, procedures for forming plans, mechanisms for evaluating activities. However, in real combat conditions, often the choice of only the functions of stimulation or only the change of the functioning parameters of the elements does not provide a coordinated interaction between the elements in the system.
This is due to the fact that the stimulation
functions and parameters can vary in a certain
limit, and this does not allow to fully reconcile the
interests of the elements in the system [
The papers of many specialists are devoted to
the issues of combat effectiveness assessing in
general and interaction directly, as well as the
search for effective forms of its implementation.
[
Therefore, further developing of active systems coordinated management methods is important, basing on the simultaneous definition of incentive functions and variables, the implementation of which provides each element of additional effect that compensates for possible losses in the implementation practice of the higher-level element plan in the management of real combat systems.
The following methods were used in the research: analysis of theoretical sources based on the organization of interaction problems, study and generalization of best practices in the organization of interaction between the elements of active systems and the method of synthesis.
To analyze the costs required to reconcile the
interests of the elements in the system, it is
possible to develop a unified approach. The article
investigates the additional (synergetic) effect that
the system and its elements receive due to
coordinated interaction, as well as the loss of each
element while performing a common task.
However, the implementation of coordinated
interaction in the system is possible only if the
additional (synergistic) effect of all elements of
the coordinated interaction exceeds their losses. If
the additional (synergetic) effect is less than the
losses, then the coordinated interaction in the
system at these parameters is inefficient and the
elements must perform their missions separately
[
The study of coordinated interaction is carried out on the model of a multi-element system. The model studied in the article includes the upperlevel control subsystem - the command center and the lower-level controlled subsystems - active combat elements from the ADA and AD Aircraft participating in combat operations according to a single plan. The command center coordinates the work of the elements by giving them a plan, missions and incentives (comprehensive support), and active combat elements carry out the
The following concepts and designations necessary for formation of conditions of the coordinated interaction between the command center and combat elements are entered: ∈ – planned state of the nth combat element, = ∈ – the actual state of the nth combat element; = ( 1, … , ) ∈
– the vector of combat elements planned states set by the command = ( 1, … , ) ∈ elements actual states;
=1 – the set of allowable values of the combat elements states; ( ) ∈ – the objective function of nth combat – the vector of combat ( ) = ( 1( 1), … , ( )) ∈ combat elements objective functions; – the vector of = ∏
=1 elements objective functions;
– the set of values of the combat locally-optimal states of the nth combat element; ∈ ( ) – the set of =1 ( ) – the set of the system locally-optimal states; of the objective function for the nth combat ∈ ( ) – the maximum value combat
element ∆ ( ) = ( )− ( ) associated
with –losses of implementation of the command center plan; nth the ̅1̅,̅̅̅; center;
= ∏ element; ( ) =
( ) = ∏ ( ) = element; – the command center objective coordinated interaction; ( , , ) = ( )− ( , , )– the command
=1 ( , ), moreover, the set of stimulating effects that provides the maximum of the objective function of the nth combat element is expressed as: ( , ) = { ( , ) ∈ |∀ ∈ , },
( , , ) ≥ ( ) and ( , ) ∈ – stimulating effect obtained by nth combat element (see Figure 1), where – the allowable set of stimulating effects functionson nth combat element; ( , ) = ( 1( 1, 1), … , ( , )) ∈ – the vector of stimulating effects, where – the set of its types; ( , , ) = ( )+ ∆ ( , , ) – the objective function of nth combat element including (supply) in the -th plan ∆ ( , , )– change in the nth combat element objective function, caused by the stimulating its
stimulation implementation; effect; ( ) ∈ ( ) = function and its possible values set ; command center objective function; ∈ ( )– maximum value of the
( )– the set of the system optimal ( ) = plans as a whole; ( ) =
∈ ( ) ( )– the value of the command center objective function on the set of locally optimal states of its elements;
( ) = ( )− ( )– additional (synergetic) effect obtained by the command center from the will take the form: ( , , ) = { ( , ) ∈ |∀ ∈ , ( ) ≥ ( , , ) }.
The set of interaction mechanisms, therefore, must be selected both in terms of the command center objective function, and in terms of the combat elements objective functions. For this purpose, the intersection of the stimulating influences sets coordinated on the general plan from a position of objective functions of combat elements ( , )is necessary, as well as the set of command 0. functions ( , , )that is ( , ) supply of troops, or stimulating actions can be implemented indirectly, by changing the various parameters of the combat elements operation models, for example, by redistributing targets between combat elements.
When used
as compensatory stimulation functions, the combat elements objective functions will be as follows: stimulating effects, ( , , , ) = ( , )+ ( , ) (3) The value ( , ) = { ( ),
= 0, ≠ is a stimulating effect obtained by nth combat element in the case of the command center planned missions
∈ ( ).
In this case, the set of stimulating functions combat elements, will be as follows: ( )which take into account the interests of ( ) = { ( )| ( ) ≥ ( ), ∈ ( ) }.
(4)
And a set of stimulating functions that take into account the interests of the command center will look like: ( ) = { ( )| ( ) ≥
∑ ( ) ≥ 0}. (5)
For the case when the stimulation is carried out by parametric coordination, the vector of coordinating parameters for each combat element is presented as: ( , ) =
+ ( , ), where – nominal value of the parameter; (6) =1 ( , ) = { ,
= 0,
≠
Moreover component of the
parameter, which is the coordinating influence of the command center on the nth combat element ( = ). the objective function of nth combat element, which takes to account parametric coordination in the implementation of various states , where – variable ( , , ) = { ( , ),
= 0, ≠ – change in the objective function of the nth command element, caused by changing the parameters by the value of during the implementation of the combat element planned task .
The set of coordinating influences ( ), takes into account the interests of combat elements and must meet the following ratio: where rn , rn – the lower and upper values of changing of the coordinating parameter for the nth combat element.
And the set of coordinating influences that take into account the interests of the command center ( )
( = { ( , ) ∈ | ≤ ≤ , , ) ≥ ( ) } , (7)
∈ | ≤ ≤ , ( ) ≥ ∑ ( =1 ( , ) , ) } .
(8)
To implement coordinated interaction, it is necessary that many ( )}, = ( , )| { and the set of incentives that take into account the interests of the command center is equal to: ( ) = + ∑ =1 ( )
Implementation of the coordinated interaction mechanism in the system is possible if: ( ) ( ) ≠ 0 (13) ( ) ≥ ( ( , ), ) + }.
(12)
The choice of the coordinated interaction model will provide an opportunity to assess the excess of additional (synergistic) effect of all system elements over their losses and the ability to calculate the effectiveness of interaction for the rational choice of its methods and implementation. That gives following opportunities:
- it is possible to predict the final result of joint actions taking into account the impact of the options of the organization of interaction of troops and their combat elements, in order to choose the best option of interaction;
- the influence of control and feedback with combat elements on the result that can be achieved is determined.
Depending on the available time and the required accuracy of the results, the computing power of simulation systems, the proposed model may take into account more factors, or vice versa, may be simplified to obtain a rougher but faster forecast of the results of troops joint actions.
This paper was created at the Anti-Aircraft Missile Troops Department of Aviation and Air Defense institute by Dmytro Rieznik, Mykhailo Levchenko, Valerii Patalakha, Serhii Kitik, Bohdan Shkurat and Oleksandr Globa.