=Paper=
{{Paper
|id=Vol-2763/CPT2020_paper_s7-9
|storemode=property
|title=Axiomatic basis and methods for interpreting conflict situations in an urgent computing environment
|pdfUrl=https://ceur-ws.org/Vol-2763/CPT2020_paper_s7-9.pdf
|volume=Vol-2763
|authors=Yuri Nechaev,Vladimir Osipov,Victor Baluta
}}
==Axiomatic basis and methods for interpreting conflict situations in an urgent computing environment==
https://ceur-ws.org/Vol-2763/CPT2020_paper_s7-9.pdf
Axiomatic basis and methods for interpreting conflict situations in an
urgent computing environment
Yu.I.Nechaev1, V.P.Osipov2, V.I.Baluta2,3
nyui33@mail.ru | Osipov@keldysh.ru | Vbaluta@yandex.ru
1
Saint Petersburg state Maritime technical University
2
Keldysh Institute of applied mathematics, Russian Academy of Sciences
3
Plekhanov Russian University of Economics
The article deals with the issues of developing an axiomatic basis and interpreting conflict situations in conditions of high uncertainty
based on the dynamic theory of catastrophes. Control over conflict situations is provided using applied modeling at the expense of the
supercomputer center through system integration of technologies and tools for processing large amounts of current information.
Functional components of the center for applied simulation implement dynamic visualization and development of management decisions.
The key factor in ensuring the safety of critical facilities in a complex conflict situation is the speed of assessment of the situation and
the development of adequate management decisions for the implementation of the response. Adequate management is based on
experience, as a rule, obtained experimentally in the course of physical modeling of impacts (exercises, trainings, experiments, etc.),
and accumulated in the form of a knowledge base of the information and analytical decision support system of the center for applied
simulation.
Key words: basis, axiomatics, axiomatic basis, interpretation, interpretation methods, conflict situations, urgent calculations.
1. Introduction activities to form scientific representations for solving
applied problems in the field of conflictology. The
The purpose of experimental studies conducted in the development of effective management decisions is
development of functional elements of the center for implemented on the basis of the formalization of
applied simulation (CAS) is to study the features of antagonistic conflicts within the framework of problem-
conflict interaction in the system of complex security of oriented methods that allow us to determine the causes of
critical objects based on Urgent computing System (UCS). conflict situations as a result of experimental studies and
At the same time, a typical situation is when due to high practical observations. Problems of this type are
uncertainty, the characteristics of the control object (CO) commonly called inverse problems [2]. Causal inverse
of interest are not available for direct observation and problems of the emergence and development of conflict
measurement, and obtaining data from a physical situations are individual and are used in the construction
experiment can be quite difficult and expensive. In this of mathematical models of interaction based on the
case, by analyzing and generalizing materials describing dynamic theory of catastrophes [3].
conflicts of various origins, some indirect information
about the object of conflict interaction under study is 2. Space behavior and management in the
obtained. Such information is determined by the nature of interpretation of conflict situations in CAS
the phenomenon being studied, the peculiarities of the models
process of origin, formation and development of various
forms of antagonistic conflicts. The identification and The procedure for solving problems involving the
formalization of conflict behavior entities of interacting reversal of causal relationships is often associated with
parties makes it possible to develop a software and tool set overcoming complex mathematical difficulties. The
for high-performance computing based on a CAS. success of the solution is determined not only by the
Diagnostics of the object of interaction is provided by quality and quantity of information obtained from the
system integration of methods of planning and conducting experiment, but also by the way it is processed. That is
computational experiments in order to further solve why the developed conceptual solutions based on the
problems related to the formation of scientific ideas and dynamic theory of catastrophes provide for the use of
the development of effective management decisions in procedures for geometric and analytical interpretation of
conflict situations. The theoretical basis for the study of the CO behavior using specially developed mathematical
conflict situations and certain methodological principles models, including modified Mathieu and Duffing
for the study of complex systems in high-performance differential equations [3]. At the same time, the solution of
environments urgent computing are formulated in [1-26]. the inverse problem in complex conflict situations is
A characteristic feature of the interpretation problems that preceded by a study of the properties of the direct problem
arise in this case is that in the course of research, it is based on a conceptual analysis [4-8]. It is assumed that the
necessary to conclude about the properties of the CO in a source data has large dimensions (a set factors and states
conflict situation based on their indirect manifestations, of CO), does not always follow the normal distribution,
established as a result of a series of computational and is incomplete, inaccurate, and noisy. Usually the data
experiments. is extremely difficult to establish as a result of specially
Thus, the CAS formulates and solves complex organized physical modeling and the only way to obtain
interdisciplinary problems associated with the creation of them is a computational experiment. The given
an integrated computer modeling system based on a characteristic of the initial data allows us to formulate the
multiprocessor computer complex, combining information following basic requirements for the mathematical model
and computational resources of expert and research
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY
4.0)
of interaction when performing urgent calculations in a These two requirements determine the construction of
CAS: an interaction model when developing algorithms for
• meaningful interpretability using the concept of Soft conflict control and testing knowledge models that define
Computing and Data Mining based on the geometric UCS procedures under various interaction conditions.
and analytical components of the dynamic disaster For fig.1 presents a conceptual framework of
model; supercomputer technologies that implements information
• efficient computability based on parallel information transformation procedures for interpreting the behavior of
processing algorithms in a multiprocessor objects in conflict situations based on the dynamic theory
supercomputer computing environment. of catastrophes.
Reference model of AXIOMATIC BASIS OF SUPER- Controlling and
conflict situations COMPUTER TECHNOLOGIES Interpreting Models
Standard Conceptual model of Analysis of the
situations information transformation current situation
Non-standard Variety of adaptive control Prediction of the
situations strategies current situation
A LOT OF ELEMENTS IMPLEMENTING A MODEL OF CONFLICT SITUATIONS
BASED ON THE DYNAMIC THEORY OF CATASTROPHES
Variety of Elements of the The set of values of the Variety of processing
operational database and input actions vector information algorithms
knowledge
Fig. 1. Axiomatic basis of supercomputer technologies for interpreting dynamic situations based on UCSUCS
The model of conflict situation interpretation in this problem in the framework of dynamic catastrophe theory,
figure is presented in the form of an interaction area, in the unified fundamental apparatus for the study of
which information transformations are performed and its nonlinear systems is preserved. In complex situations,
geometric representations are constructed, which allow us especially in non-stationary interaction, in addition to the
to understand the processes of learning and development usual behavior and control spaces, the corresponding
and identify the "subtle effects" of the studied functions that characterize the variety of conflict situations
phenomenon. The cognitive process provides under study are considered.
"compression" of the code of the processed signal and Thus, the CAS in the interpretation of conflict
maximum possible abstraction of the description situations is considered as a developing active dynamic
contained in the signal to achieve a higher degree of system functioning in a complex dynamic environment.
predictability [4]. Management of CAS is to establish the procedures,
The concept of dynamic catastrophe theory defines the minimizing an objective function that ensure the maximum
study of CO behavior within the framework of spatio- effectiveness of management in the current situation.
temporal interpretation. The formal model for converting Active elements are defined as CAS objects whose
information based on UCS procedures looks like: functions are aimed at modeling and visualizing the
{R1n ( t ) × R1r ( t ) → R1 ( t ) ,..., Rmn ( t ) × Rmr ( t ) → Rm ( t )} , (1) dynamics of interaction between elements of a conflict
where {R1n(t),...,Rmn(t)} and {R1r(t),...,Rmr(t)} - spaces of environment within the framework of the UCS concept.
behavior and control that determine the result of the When generating alternatives and developing control
transformation of information about the conflict on the actions, a collective strategy is selected, taking into
account the strategy of the active elements of the multi-
basis of which the reconstruction of the original formal
models of interaction; j = 1,...,m - the sequence of events agent system (MAS). The hypothesis of independent
that define the evolution of the system. behavior of active elements (intelligent agents-IA) is
The model is used as an operator for nonlinear considered within the framework of the paradigm of
transformation of information about the evolution of the information processing in a multiprocessor computing
CO: environment [3]. The synthesis of an optimal control
function for active elements of distributed intelligence
f j ( • ) : R nj ( t ) × R rj ( t ) → R j ( t ) , MAS ensures maximum efficiency of information
(2)
where Rjn(t), Rjr(t), Rj(t) are spaces of internal and external processing procedures in UCS mode. Multiple actions to
variables controlled by the function f(•), which can be implement IA in the Multiagent Modeling System (MMS)
considered as a smooth function taking into account the is defined by a set of decision support procedures (DPS).
accepted assumptions. Planning actions in assessing the state of the CO and
To display the results of the functioning of the CPM predicting its development in the MMS consists in
using the function fj(•), quasi-stationarity sections are choosing effective planning procedures based on the
considered in the process of evolution of the interaction criteria of optimality [4].
system. The physical interpretation of the features of CO We formalize the problem of evaluating the
behavior in these areas is carried out within the framework effectiveness of the developed management decisions in
of synergetic control theory [9]. When discussing this the CAS models. Let x∈Rn be the vector of parameters
defining the generated solutions, and w∈Rm be the vector or serial connection S = S1 ⊗ ... ⊗ Sk subsystems Si
of the state of the conflict interaction environment in 𝜃𝜃(𝑆𝑆) ≤ 𝜃𝜃(𝑆𝑆1 ) + ⋯ + 𝜃𝜃(𝑆𝑆𝑘𝑘 ). (9)
which the controlled CO functions. If [x, w]∈A, then the Axiom 3. If the dynamic behaviorin volves a feedback
technical solution with the parameter vector x ensures the connection (Σ-1) from system S2 to system S1, then
effective functioning of the CO in an environment 𝜃𝜃(𝑆𝑆1 ⊕ 𝑆𝑆2 ) ≤ 𝜃𝜃(𝑆𝑆1 ) + 𝜃𝜃(𝑆𝑆2 ) + ⋯ + 𝜃𝜃(𝑆𝑆2 (𝛴𝛴 −1 )𝑆𝑆1 ).
characterized by the vector w. If [x,w]∈B then the (10)
generated solution leads to inefficient operation of the Obviously, axiom 3 is a special case of axiom 2 if there
system. These conditions define the problem of choosing are no feedbacks.
a solution: If in the class of systems satisfying axioms 1-3, a
( )
х * X , W > 0, ∀(X, W) ∈ A ; subset of systems ϕ is distinguished, then the
normalization condition is satisfied:
( )
х * X , W < 0, ∀(X, W) ∈ В , х*∈ Х * , (3) 𝜃𝜃(𝑆𝑆) = 0 ∀𝑆𝑆 ∈ 𝜙𝜙. (11)
where x* is the selected class of dividing functions. Thus, the complexity of CAS elements is a multi-
When conditions (3) are implemented, the CAS valued concept that includes static and dynamic
models establish a range of possible values for controlled components. Static complexity is determined by the
CO parameters, which is limited by various factors, complexity of subsystems, and dynamic complexity is
including the specifics of functioning and the level of determined by the generation of control signals.
development of intelligent technologies. Each specific Management software is supported by a level of
implementation of a technical solution corresponds to computational complexity. A group of operators
certain values of parameters that meet the conditions [10]: "interpretation - action" forms a structure of
𝑋𝑋1min ≤ 𝑋𝑋𝑖𝑖 ≤ 𝑋𝑋𝑛𝑛max , 𝑖𝑖 = 1, … , 𝑛𝑛. (4) transformations on a set of generated management
Thus, in the n-dimensional parameter space for each decisions in order to develop a General concept of
implementation, a parameter vector can be represented managing a complex system of conflict interaction.
𝑋𝑋 = (𝑥𝑥1 , … , 𝑥𝑥𝑛𝑛 )𝑇𝑇 , (5) Complexity theory is a prerequisite for understanding
which belongs to the parameter space defined by learning and development processes, and a hierarchical
inequalities (4). structure defines management under conditions of time
The parameter vector (5) uniquely defines the delays, noise and uncertainty.
characteristics of the CO, the set of which is denoted by Since a CAS system can be represented as
(Ch)j, j=1,…,m. The number of characteristics is sequentially-parallel or cascaded (hierarchically)
determined by the CO functionality and features of the connected subsystems, including subsystems with
conflict situation. feedback, the axioms of connectivity explain the structure
We will match each set of CO characteristics with a of such decompositions. Thus, the hierarchical system in
vector question is complex and organized. Complexity is defined
𝐻𝐻 = ((Ch)1 , … , (Ch)𝑚𝑚 )𝑇𝑇 (6) as the minimum number of operations required to restore
m-dimensional space of interaction. the system, and organization is defined as the ability to
In this case, technically, the CO can be considered as a "compress" information generated by a cascade of
certain system that has ninputs for parameters xi and bifurcations that lead to symmetry breaking, and after the
moutputs for interaction characteristics (Ch)j. For each onset of chaos - by a cascade of iterations that increase the
vector X of the parameter space (5), such a system matches resolution of the display at a given time interval.
the vector of the technical characteristics space defined by Within the framework of the axiomatic approach, the
the relation (6). recognition of abnormal behavior of the CO during the
The considered CO model allows us to construct a operation of the CAS based on the UCS concept is
geometric interpretation of various variants of problems, implemented using the following procedures:
their analysis and optimal design of operations in the CAS Procedure 1. Classes of abnormal behavior of objects
system. in a conflict situation are identified and the corresponding
reference interactions are studied using the use-case
3. The axiomatic basis of the system knowledge base.
complexity elements of the CAS Procedure 2. An analysis of the conflict situation
The main aspects of the system analysis of structural under study is performed, based on which fragments of
components S of the CAS reflect the measure of interacting objects are formed that are close to classes of
complexity θ(S) of the system: hierarchy, connectivity and abnormal behavior.
dynamic behavior, expressed in the following axioms [11]. Procedure 3. For the selected fragments, an axiomatic
Axiom 1..Hierarchy defines the occurrence of basis is formulated in the form of a sequence of axioms
subsystem S0 in the system S as an inequality corresponding to the reference trajectories.
𝜃𝜃(𝑆𝑆0 ) ≤ 𝜃𝜃(𝑆𝑆), (7) Thus, the problem of recognizing abnormal CO
in other words, a subsystem cannot be more complex than behavior based on UCS s reduced to the problem of fuzzy
the system as a whole. search for fragments of reference interactions of abnormal
Axiom 2. Connectivity characterizes parallel behavior in the observed system evolution.
connection The mathematical theory of functional space in UCS is
defined by a system of objects and relations within the
S = S1 ⊕ ... ⊕ Sk subsystems Si
framework of an ontological basis, and the logical
𝜃𝜃(𝑆𝑆) = max𝜃𝜃(𝑆𝑆𝑖𝑖 ), 𝑖𝑖 = 1, … , 𝑘𝑘. (8)
structure of the interpretation of the dynamics of the
interaction system is based on fundamental provisions where the components X1(T,S),...,Xn(T,S) define the
(axioms) that determine the evolutionary complexity of the interpretation functions at each step of performing
CO. In this case, the analytical component of the dynamic information transformation operations using the control
catastrophe theory is represented by interpretation models, function, a and Y1(Out),...,Yn(Out) are the results of
while the geometric component is represented by various predicting the studied characteristics of the interaction
visual models in the form of cognitive images and fractal system.
maps. The problem of space-time is considered taking into One of the features of the CAS structure is a
account a measure of complexity, taking into account the hierarchical organization that defines management in
interaction of elements of a conflict situation, as well as conditions of time delays, noise and uncertainty. Strategic
the relationship of the concept of analytical synthesis with planning of operations and conceptual decisions in a
the physical laws of interaction. hierarchical organization is presented in the form of a
The task of predicting CO behavior in a conflict dynamic hierarchical network [12] (figure 2), which
situation is a chain of transformations: reflects the fundamental result of integrating components
𝑋𝑋1 (𝑇𝑇, 𝑆𝑆) ⇒ 𝑌𝑌1 (Out),..., 𝑋𝑋𝑛𝑛 (𝑇𝑇, 𝑆𝑆) ⇒ 𝑌𝑌𝑛𝑛 (Out), (12) of a dynamic disaster model based on intelligent
technologies and high-performance computing [4].
DYNAMIC HIERARCHICAL NETWORK OF
CONCEPTUAL DECISIONS
MR(S0(f,F))
MR(S0)
MR(S1(f,F))
MR(S1) MS(S11) MS(S12)
MR(S11(f,F)) MR(S12(f,F))
MR(S11) MS(S111) MR(S112) MR(S12) MR(S121) MR(S122)
Fig. 2. Structure of a dynamic hierarchical UCS network
The hierarchical model allows describing the dynamics {A1} {Ai } {An }
of a conflict situation at various levels of abstraction: . (15)
reflections of elements, properties, and characteristics that X1
(x11 )* (x1i )* (x1n )*
determine the functions of managing f interpreting F the
development of the current situation. When decomposing, Xj
(x )j1
*
(x )
ji
*
(x )
jn
*
the concept of connectivity is realized, assuming the
representation of the original model MR(S0) in the form of Xm
(xm1 )* (xmi )* (xmn )*
a set of sublevel models connected by a tree relation. The
formation of hierarchy levels is carried out using the Matrix (15) is obtained on the basis of the
standard basis decomposition. At any level of the transformation of the initial data (functional elements of
hierarchy, the CAS subsystems and relationships between the CO) using the Cartesian product {m×n} of sets of
them are distinguished, while ensuring the level of alternatives A and features X, which form a representation
complex and not losing the levels of direct analysis. of the dynamics of interaction in the current conflict
The task of constructing an optimal hierarchical situation. The system of alternatives in the resulting matrix
structure is to construct a set Ω hierarchical structures of strategic decisions is reduced to a single scale using the
(hierarchies) with a given functional transformation
∗
argmin𝐺𝐺 ∈ 𝛺𝛺 𝑃𝑃(𝐺𝐺), (13) �𝑥𝑥ji � = �𝑥𝑥ji − 𝑥𝑥min𝑗𝑗 �/�𝑥𝑥max𝑗𝑗 − 𝑥𝑥min𝑗𝑗 � (16)
𝑃𝑃: 𝛺𝛺 → 𝐺𝐺 [0, +∞]. (14) with display
The concept of hierarchical structure implies the 𝑥𝑥ji → 𝑥𝑥 ∗ ∈ [0, 1]. (17)
asymmetry of connections and the impossibility of cyclic Matrix (15) is used to construct matrices that display
subordination, i.e., the oriented graph and its acyclicity. interpretation functions in behavior spaces (Int-Beh) and
As a tool for describing Ci CAS tasks and the order of control spaces (Int-Cont) at a given implementation
their distribution on the basis of the functional space of interval:
behavior of the dynamic theory of catastrophes, the matrix {𝐴𝐴(Int − Beh)}
of strategic decisions is used, which is an extension of the 𝑓𝑓1 ⋯ 𝑓𝑓𝑖𝑖 ⋯ 𝑓𝑓𝑛𝑛
functionality of the presentation [13]: 𝑓𝑓 ⋯ 𝑓𝑓𝑖𝑖1 ⋯ 𝑓𝑓𝑛𝑛1 (18)
� 11 �
⋯
𝑓𝑓1𝑚𝑚 ⋯ 𝑓𝑓im ⋯ 𝑓𝑓nm
{𝐴𝐴(Int − Cont} the CO and predicting its development consists in
𝐹𝐹1 ⋯ 𝐹𝐹𝑖𝑖 ⋯ 𝐹𝐹𝑛𝑛 choosing effective planning procedures based on optimal
𝐹𝐹11 ⋯ 𝐹𝐹𝑖𝑖1 ⋯ 𝐹𝐹𝑛𝑛1 criteria
� � The task of modeling CO dynamics is to construct
⋯
𝐹𝐹1𝑚𝑚 ⋯ 𝐹𝐹im ⋯ 𝐹𝐹nm scenarios (situation models) with a dynamically changing
The initial information for constructing the matrix of class of strategies and manage the scenario. To solve the
strategic decisions is the information transformation problem, a scenario SC is formed, the execution procedures
model M (Inf), which contains the following data sets [3, of which consist in representing SC as a combination of
4]: strategies (alternatives) Sctj and control moments tj,
M ( Inf ) =< Cond ( D),V ( D), M (С ) > (19) (j=1,...,N)
𝑡𝑡𝑗𝑗
where Cond (D) is a vector of terms that defines a set of 𝑆𝑆𝐶𝐶 = 𝑌𝑌 𝑆𝑆𝐶𝐶 . (20)
𝑡𝑡𝑗𝑗
conditions for the existence of solutions X = {X1, Xn}; Transitions between PS strategies are described by
V(D) is a vector of decisions that includes the set of mapping the set of effective strategies as two sets, the first
solutions Y ={Y1, ...,Ym}; M(C) - matrix of compliance of which corresponds to the set of arcs, and the second to
specifying model relationships between conditions and the set of benefits of these strategies in the set of arcs.
decisions. The crucial rule for choosing alternatives in the multi
This interpretation of data reflects the principle of criteria optimization problem is represented by the
complementarity, according to which conditions are intersection of fuzzy goals Gi and constraints Cj or a
provided in which there is a continuous change in the convex combination taking into account their relative
behavior of objects in the conflict environment. The importance:
formal model of information transformation opens up the 𝐷𝐷 = 𝐺𝐺1 ∩ … ∩ 𝐺𝐺𝑖𝑖 ∩ 𝐶𝐶1 ∩ … ∩ 𝐶𝐶𝑗𝑗 … ; 𝐷𝐷 =
possibility of finding solutions using hierarchical (21)
∑𝑖𝑖 𝛼𝛼𝑖𝑖 𝐺𝐺𝑖𝑖 + ∑𝑗𝑗 𝛼𝛼𝑗𝑗 𝐺𝐺𝑗𝑗 , ∑𝑖𝑖 𝛼𝛼𝑖𝑖 + ∑𝑗𝑗 𝛼𝛼𝑗𝑗 = 1,
structures that are characteristic of the tasks under study.
where α is the importance coefficient.
This model does not depend on the content of the problem
and is a universal tool for analyzing and finding solutions. 4. Strategies for interpreting CO behavior
This opens the possibility of "compressing" information, based on the UCS concept
since only the information that is minimally necessary for
managing a conflict situation is extracted from the source In accordance with the concept of dynamic catastrophe
data. theory on the basis of a supercomputer complex CAS a
Thus, the CAS is considered as an active system strategy for interpreting the evolution of the CO is
functioning in a complex dynamic environment of implemented as the ability to transform a set of input
interacting objects. Management of MTC is to establish signals into a set of output signals in the form of a formal
the procedures, minimizing an objective function that model:
ensure the maximum effectiveness of management in the 𝐺𝐺(Attr) = ⟨𝐺𝐺(Stab), 𝐺𝐺(Cap)⟩, (22)
current situation. Active elements are defined as CAS where G(Attr) - attractor sets, displaying a model of
objects whose functions are aimed at modeling and interaction in a hostile environment Oh; G(Stab) - many,
visualizing the dynamics of a conflict environment within forming a movement CO to the target attractor; G(Cap) -
the framework of the UCS concept . When generating set, characterizing the behavior of the CO in the loss of
alternatives and developing control actions, a collective stability of the environment.
strategy is selected, taking into account the strategy of the The CAS computing complex implements the input-
active elements of the system. The hypothesis of output operator behavior functions and provides solutions
independent behavior of active elements of the CPU is to identification, approximation, and prediction problems
considered within the framework of the paradigm of that determine the behavior of the CO in the process of
information processing in a multiprocessor computing evolution. The interaction space within the framework of
environment. The synthesis of an optimal control function dynamic catastrophe theory defines the interpretation and
for active elements of the CPU ensures maximum control functions, which are used to carry out operational
efficiency of information processing procedures. The set control of the characteristics of an aggressive environment
of implemented actions is determined by the set of PPR in the course of evolution (Fig. 3).
procedures. Planning actions when assessing the state of
Iterative process of information transform in the implementation of the dynamic
theory of catastrophes
A priori Interpretation Control function
information function
Simulated situation Allocation of data Allocation situation
structures signs
Simulation results Generalizing Model Select management
Classes structure
Measurement results System state Formation of
evaluation management function
Fig. 3. Converting information based on the UCS concept
The General formal knowledge model integrating the π (S ) = f j (•) ∆t1 ,, f n (•) ∆t n , (24)
used classes of conflict situation interpretation
functionsbased on UCS is presented as a functional: where fj(•) is the control law defining the expansion and
Φ 1 { f1 (•) µ },, Φ 5 { f (•) µ }, (23)
contraction phases depending on the state interpretation
function at the j-th stage of the system evolution (j=1,...,n);
where Фj{f(•)| µ}, (j=1,..., 5) - functions that define classes ∆tj is the duration of the stages.
of interpretation models: Ф1{f(•)|µ} and Ф2{f(•)|µ} - The implementation of interpretation and control
computational and diagnostic models; Ф3{f(•)|µ} - models functions is carried out when modeling the behavior of an
defining the strategy of dynamic catastrophe theory; CO based on the UCS concept (Fig.4). The CO behavior
Ф4{f(•)|µ} - models for analyzing and predicting the model is constructed using MAC and neuro-dynamic
current situation; Ф5{f(•)|µ} - models of a dynamic systems (ND-systems) oriented to parallel processing of
knowledge base. information in a supercomputer environment of the CAS
The construction of the control function at each step of [3, 4].
the iterative procedure is based on the synergetic paradigm
π(S) in the form of a sequence of actions:
MODELING OF BEHAVIOR IN CONFLICT SITUATIONS
Implementation of multi-agent and
Link functions
neurodynamic systems in order to represent
and system
the mechanisms of behavior of objects in the
operations
interaction environment
Functions of the Controlling the behavior of system objects
training system and based on a learning strategy and generating
their optimal implementation algorithms
implementation
Fig. 4. Modeling behavior in CO interpretation based on UCS
The theory of strategic decisions in managing CO of actions, but at the level of chains of events. To perform
behavior provides for a transition from situational simulation procedures in the created virtual space, abstract
management to management with modeling. Relationships symbols of various classes of elements of the structure of
in graph-based interpretation of network models allow us an aggressive environment are formed and the ability to
to take into account the consequences of decisions being interpret its behavior within the framework of the theory
made and control the behavior of the CO not at the level of synergetic control is formed.
The facts and phenomena of CO modeling are related based on the concentration of "consciousness" on the most
to various interpretations of activity in solving behavior important aspects of the development of the interaction
training tasks using simulations of the physiological and process, which reflects the evolution of the conflict
mental functions of objects in a conflict situation. The environment within the framework of a dynamic model of
functions of sensory systems are implemented in the catastrophes (Fig.5) [3].
construction of algorithms for information processing
КОНЦЕПТУАЛЬНАЯ МОДЕЛЬ ЭВОЛЮЦИИ КОНФЛИКТНОЙ СРЕДЫ
Interpreting activity Building and using functional analysis models
Information processes Representation of the environment evolution
based on the dynamic model of catastrophes
Sensor systems Functions of sensory systems in algorithms of
concentration of "consciousness"
Fig. 5. Evolution of the interaction system based on dynamic catastrophe theory
The concept of a training model as a mechanism for
coordinating the activity of interaction processes of 5. Assessing the adequacy of conflict situation
conflict objects and the overall balance of information interpretation models based on the UCS
processing procedures of a supercomputer CAS ensures concept
the fulfillment of the main modeling. It's task is to create a Let's consider the features of the functioning of the
computing environment for virtual modeling of CAS software complex based on the dynamic theory of
information-physical processes that run in parallel and catastrophes. The conceptual model of assessing the
ensure the organization of information exchange between adequacy of mathematical models describing the system
processes (synchronization), and also decision support in of interaction of objects in conflict situations formalizes
a complex dynamic environment. The controlling the processes of constructing problems and criteria
influence that changes the state of the CO in accordance functions for interpreting the evolution of the CO in the
with a given law is described using the relations: implementation interval. For rice.6 presents a sequence of
𝑦𝑦0 (𝛬𝛬(𝜋𝜋)0 ),..., 𝑦𝑦𝑘𝑘 (𝛬𝛬(𝜋𝜋)𝑘𝑘 ). (25) information processing operations that determines the
Here y(Λ(π)) −(π) is a vector of parameters (π0,...πk) criteria basis for evaluating the adequacy of mathematical
that define the characteristics of the environment and description of interaction processes in conflict situations.
perturbing influences for a given CO evolution in
accordance with the operating modes of the CPU within
the permissible "input - output" region.
CONCEPTUAL MODEL FOR ASSESSING THE ADEQUACY OF FUNCTIONING OF
THE INTERACTION SYSTEM OF CONFLICT ENVIRONMENTAL OBJECTS
Identification Recovery of external disturbances of the
interaction environment
Approximation Assessment of the characteristics of the
controlled object (interaction parameters)
Prediction Predicting the behavior of a controlled object
(stages of evolution)
Fig. 6. Criteria basis for implementing UCS procedures in a conflict situation
Here the main stages of implementation of (figure 7) defines the formalization of the conflict situation
computational technology for determining the parameters based on the factors that characterize a priori information,
of an aggressive environment, dynamics of interaction of the concept of the minimum description length (M DL),
environmental objects, as well as the stages of evolution in and the problem of complexity. Here the sequence of
predicting the behavior of elements of the modeled system stages of forming an adequate UCS model within the
are highlighted. framework of the MDL concept [14] and complexity
The strategy for assessing the adequacy of UCS theory [15] is indicated.
procedures in the functioning of the computing complex
A priori information MDL concept Complexity problems
Dynamic Formation of an Forming a set
measurement data information array of models
Physical simulation Selection of data Selection of models
results structures based on criteria
Results of Estimation of the Assessment of the
mathematical description error adequacy of the
modeling model
Fig. 7. Information flow that determines the strategy for evaluating the adequacy of the interaction model when interpreting dynamic
situations based on UCSUCS
As follows from this figure, the problem of adequacy The assessment of UCS adequacy is based on a
is solved by integrating a priori information, the concept modified scheme of O. Balchi [4] for a specific application
of MDL and the problem of complexity, which determines of the conflict situation in order to take into account the
the choice of a solution in accordance with the conceptual data of physical, neuro-fuzzy and neuro-evolutionary
model of dynamic catastrophe theory [16], which is modeling (Fig.8).
adapted in relation to the problem under consideration.
Neural fuzzy Version M Model Version M
modeling
3 construct
3
Neuro
Evolutionary
modeling
4 Using a physical 2 Parametric
synthesis
Model research
4 Using a physical 2 Correlation
analysis
experiment experiment
Generation and Structural Assessment of Analysis of
analysis of
alternatives 5 1 synthesis adequacy 5 1 variance
Cycle М – ND-model Cycle М – standard model
Computational Version S Model Version S
experiment
3 analysis
3
Generation and
analysis of
alternatives
4 Selection and 2 Selection of NF,
NE models
Improving the
model 4 Selection and 2 Model selection
analysis of the analysis of the
preferred model preferred model
Assessment of Bank analysis of Assessment of Formation of an
adequacy 5 1 ND-models adequacy 5 1 ensemble of
models
Cycle S – ND-model Cycle S – standard model
Construction of Version P Space of Version P
NF, NE models
3 alternatives
3
Computational
experiment 4 Hypotheses and
simplifying 2 Analysis of
Choosing a
solution 4 Using hypotheses 2 Simplifying
assumptions using results and simplifying assumptions
assumptions
Assessment of Physics Assessment of Hypothesis
adequacy 5 1 experiment adequacy 5 1 formulation
Cycle Р – ND-model Cycle Р – standard model
Fig. 8. Graph-interpretations of O. Balchi's modified scheme, in which M,S,P are cycles of information transformation
At the same time, the improvements consisted in situations in the functioning of the software complex of the
considering UCS as an integral part of a practical CAS based on the principle of competition.
application based on it - the task of modeling conflict
The first cycle is associated with the development of based on CAS and high-performance information
competing models (modeling- M), implemented on the processing tools.
basis of the ND-system and methods of classical The solution to these problems will achieve the goal of
mathematics. In the course of this cycle, the structural and creating MTC - improving the efficiency of FFD-based
parametric synthesis of the neural network is implemented simulation and visualization of the dynamics of interaction
in the tasks of neuro-fuzzy NF and neuro-evolutionary between the elements of the conflict environment on the
modeling, and for the competing model, the assessment of basis of supercomputer technologies. The conceptual
the overall structure and components within the solutions that define the problem of connectivity,
framework of sequential statistical analysis procedures. complexity and stability based on the UCS concept are
The second cycle refers to the implementation of aimed at ensuring the principle of adaptability and reflect
appropriate mathematical (simulation) experiments a single trend - an adequate description of the hierarchical
performed with competing models (simulation- S) for organization and the identification of significant
given initial conditions and input vector elements. Here functionally significant elements of interaction in a
NF and NE models of data Bank analysis are formed, on conflict situation. The above analysis is crucial in the
the basis of which a computational experiment is search for mechanisms that ensure the formation of
implemented, generation and analysis of alternatives and collective properties of interpretation of an aggressive
assessment of adequacy. Construction and analysis of the dynamic environment, leading to the formation of
competing model is carried out in accordance with the hierarchical systems and the emergence of the possibility
formalization of the problem in conditions of significant of their mutual modeling. Compression of the
uncertainty in accordance with the algorithm [3]. mathematical description of conflict situations is a
The third cycle is the most important. It consists of necessary prerequisite for the formation of collective
conducting physical (physical- P) experiments, on the properties of interaction models in UCS through the
basis of which models are formed that provide an organization of cross-correlations between the
assessment of adequacy under conditions of complete corresponding variables.
uncertainty. During ND this cycle, the components of the
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