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.
development of functional elements of the center for applied simulation (CAS) is to study the features of conflict interaction in the system of complex security of critical objects based on Urgent computing System (UCS). At the same time, a typical situation is when due to high uncertainty, the characteristics of the control object (CO) of interest are not available for direct observation and measurement, and obtaining data from a physical experiment can be quite difficult and expensive. In this case, by analyzing and generalizing materials describing conflicts of various origins, some indirect information about the object of conflict interaction under study is obtained. Such information is determined by the nature of the phenomenon being studied, the peculiarities of the process of origin, formation and development of various forms of antagonistic conflicts. The identification and formalization of conflict behavior entities of interacting parties makes it possible to develop a software and tool set for high-performance computing based on a CAS.
Diagnostics of the object of interaction is provided by
system integration of methods of planning and conducting
computational experiments in order to further solve
problems related to the formation of scientific ideas and
the development of effective management decisions in
conflict situations. The theoretical basis for the study of
conflict situations and certain methodological principles
for the study of complex systems in high-performance
environments urgent computing are formulated in [
arise in this case is that in the course of research, it is necessary to conclude about the properties of the CO in a conflict situation based on their indirect manifestations, established as a result of a series of computational experiments.
Thus, the CAS formulates and solves complex
interdisciplinary problems associated with the creation of
an integrated computer modeling system based on a
multiprocessor computer complex, combining information
and computational resources of expert and research
activities to form scientific representations for solving
applied problems in the field of conflictology. The
development of effective management decisions is
implemented on the basis of the formalization of
antagonistic conflicts within the framework of
problemoriented methods that allow us to determine the causes of
conflict situations as a result of experimental studies and
practical observations. Problems of this type are
commonly called inverse problems [
The procedure for solving problems involving the
reversal of causal relationships is often associated with
overcoming complex mathematical difficulties. The
success of the solution is determined not only by the
quality and quantity of information obtained from the
experiment, but also by the way it is processed. That is
why the developed conceptual solutions based on the
dynamic theory of catastrophes provide for the use of
procedures for geometric and analytical interpretation of
the CO behavior using specially developed mathematical
models, including modified Mathieu and Duffing
differential equations [
and analytical components of the dynamic disaster model; • efficient computability based on parallel information processing algorithms in a multiprocessor supercomputer computing environment.
an interaction model when developing algorithms for conflict control and testing knowledge models that define
supercomputer technologies that implements information transformation procedures for interpreting the behavior of objects in conflict situations based on the dynamic theory of catastrophes.
Reference model of conflict situations
AXIOMATIC BASIS OF SUPER
COMPUTER TECHNOLOGIES Standard situations Non-standard situations
Conceptual model of information transformation Variety of adaptive control strategies
Controlling and Interpreting Models
Analysis of the current situation Prediction of the current situation A LOT OF ELEMENTS IMPLEMENTING A MODEL OF CONFLICT SITUATIONS
BASED ON THE DYNAMIC THEORY OF CATASTROPHES Variety of Elements of the operational database and knowledge
The set of values of the input actions vector
Variety of processing
information algorithms
The model of conflict situation interpretation in this
figure is presented in the form of an interaction area, in
which information transformations are performed and its
geometric representations are constructed, which allow us
to understand the processes of learning and development
and identify the "subtle effects" of the studied
phenomenon. The cognitive process provides
"compression" of the code of the processed signal and
maximum possible abstraction of the description
contained in the signal to achieve a higher degree of
predictability [
The concept of dynamic catastrophe theory defines the study of CO behavior within the framework of spatiotemporal interpretation. The formal model for converting information based on UCS procedures looks like: {R1n (t ) × R1r (t ) → R1 (t ) ,..., Rmn (t ) × Rmr (t ) → Rm (t )} , (1) where {R1n(t),...,Rmn(t)} and {R1r(t),...,Rmr(t)} - spaces of behavior and control that determine the result of the transformation of information about the conflict on the basis of which the reconstruction of the original formal models of interaction; j = 1,...,m - the sequence of events that define the evolution of the system.
f j (•) : Rnj (t ) × Rrj (t ) → Rj (t ) , (2) where Rjn(t), Rjr(t), Rj(t) are spaces of internal and external variables controlled by the function f(•), which can be considered as a smooth function taking into account the accepted assumptions.
To display the results of the functioning of the CPM
using the function fj(•), quasi-stationarity sections are
considered in the process of evolution of the interaction
system. The physical interpretation of the features of CO
behavior in these areas is carried out within the framework
of synergetic control theory [
situations is considered as a developing active dynamic system functioning in a complex dynamic environment.
minimizing an objective function that ensure the maximum effectiveness of management in the current situation.
functions are aimed at modeling and visualizing the
dynamics of interaction between elements of a conflict
environment within the framework of the UCS concept.
When generating alternatives and developing control
actions, a collective strategy is selected, taking into
account the strategy of the active elements of the
multiagent system (MAS). The hypothesis of independent
behavior of active elements (intelligent agents-IA) is
considered within the framework of the paradigm of
information processing in a multiprocessor computing
environment [
processing procedures in UCS mode. Multiple actions to implement IA in the Multiagent Modeling System (MMS) is defined by a set of decision support procedures (DPS).
We formalize the problem of evaluating the effectiveness of the developed management decisions in the CAS models. Let x∈Rn be the vector of parameters defining the generated solutions, and w∈Rm be the vector of the state of the conflict interaction environment in which the controlled CO functions. If [x, w]∈A, then the technical solution with the parameter vector x ensures the effective functioning of the CO in an environment characterized by the vector w. If [x,w]∈B then the generated solution leads to inefficient operation of the system. These conditions define the problem of choosing a solution:
х * (X ,W ) > 0, ∀(X, W) ∈ A ; х * (X ,W ) < 0, ∀(X, W) ∈ В , х*∈ Х * , (3) where x* is the selected class of dividing functions.
models establish a range of possible values for controlled
including the specifics of functioning and the level of
development of intelligent technologies. Each specific
implementation of a technical solution corresponds to
certain values of parameters that meet the conditions [
= ((Ch)1, … , (Ch) ) m-dimensional space of interaction.
certain system that has ninputs for parameters xi and moutputs for interaction characteristics (Ch)j. For each vector X of the parameter space (5), such a system matches the vector of the technical characteristics space defined by the relation (6).
The considered CO model allows us to construct a
geometric interpretation of various variants of problems,
their analysis and optimal design of operations in the CAS
complexity θ(S) of the system: hierarchy, connectivity and
dynamic behavior, expressed in the following axioms [
Axiom 1..Hierarchy defines the occurrence of subsystem S0 in the system S as an inequality in other words, a subsystem cannot be more complex than ( 0) ≤ ( ), the system as a whole. connection
Connectivity characterizes parallel S = S1 ⊕ ... ⊕ Sk subsystems Si ( ) = max ( ), = 1, … , . (4) (5) (6) (7) (8) (10) (9) (11) or serial connection S = S1 ⊗ ... ⊗ Sk subsystems Si ( ) ≤ ( 1) + ⋯ + ( ).
connection (Σ-1) from system S2 to system S1, then ( 1 ⊕ 2) ≤ ( 1) + ( 2) + ⋯ + ( 2( −1) 1).
are no feedbacks.
If in the class of systems satisfying axioms 1-3, a subset of systems ϕ is distinguished, then the normalization condition is satisfied:
( ) = 0 ∀ ∈ .
Thus, the complexity of CAS elements is a multivalued concept that includes static and components. Static complexity is determined by the complexity of subsystems, and dynamic complexity is determined by the generation of control signals.
computational "interpretation complexity. action"
A forms group of
operators a structure of transformations on a set of generated management decisions in order to develop a
managing a complex system of conflict interaction.
a
CAS system can be represented as sequentially-parallel or cascaded (hierarchically) connected subsystems, including subsystems with feedback, the axioms of connectivity explain the structure of such decompositions. Thus, the hierarchical system in question is complex and organized. Complexity is defined as the minimum number of operations required to restore the system, and organization is defined as the ability to "compress" information generated by a cascade of bifurcations that lead to symmetry breaking, and after the onset of chaos - by a cascade of iterations that increase the resolution of the display at a given time interval.
recognition of abnormal behavior of the CO during the operation of the CAS based on the UCS concept is implemented using the following procedures:
basis is formulated in the form of a sequence of axioms corresponding to the reference trajectories.
of recognizing abnormal CO behavior based on UCS s reduced to the problem of fuzzy search for fragments of reference interactions of abnormal behavior in the observed system evolution.
defined by a system of objects and relations within the framework of an ontological basis, and the logical structure of the interpretation of the dynamics of the interaction system is based on fundamental provisions (axioms) that determine the evolutionary complexity of the CO. In this case, the analytical component of the dynamic catastrophe theory is represented by interpretation models, while the geometric component is represented by various visual models in the form of cognitive images and fractal maps. The problem of space-time is considered taking into account a measure of complexity, taking into account the interaction of elements of a conflict situation, as well as the relationship of the concept of analytical synthesis with the physical laws of interaction.
The task of predicting CO behavior in a conflict situation is a chain of transformations: 1( , ) ⇒ 1(Out),..., ( , ) ⇒ (Out), (12) where the components X1(T,S),...,Xn(T,S) define the interpretation functions at each step of performing information transformation operations using the control function, a and Y1(Out),...,Yn(Out) are the results of predicting the studied characteristics of the interaction
One of the features of the CAS structure is a
hierarchical organization that defines management in
conditions of time delays, noise and uncertainty. Strategic
planning of operations and conceptual decisions in a
hierarchical organization is presented in the form of a
dynamic hierarchical network [
basis decomposition. At any level of the hierarchy, the CAS subsystems and relationships between them
are distinguished, while ensuring the level of complex and not losing the levels of direct analysis.
structure is to construct a set Ω hierarchical structures (hierarchies) with a given functional argmin ∈ ( ), :
→ [0, +∞].
asymmetry of connections and the impossibility of cyclic subordination, i.e., the oriented graph and its acyclicity.
As a tool for describing Ci CAS tasks and the order of
their distribution on the basis of the functional space of
behavior of the dynamic theory of catastrophes, the matrix
of strategic decisions is used, which is an extension of the
functionality of the presentation [
* (x j1 )* (xm1 ) * {Ai } (x1i )* (x ji )* (xmi ) * {An} (x1n )* .
(x jn )* (xmn )* Matrix (15) is obtained on the basis of the transformation of the initial data (functional elements of the CO) using the Cartesian product {m×n} of sets of alternatives A and features X, which form a representation of the dynamics of interaction in the current conflict situation. The system of alternatives in the resulting matrix of strategic decisions is reduced to a single scale using the = ji − min / max − min
ji → ∗ ∈ [
Matrix (15) is used to construct matrices that display interpretation functions in behavior spaces (Int-Beh) and control spaces (Int-Cont) at a given implementation interval: 1 where Cond (D) is a vector of terms that defines a set of conditions for the existence of solutions X = {X1, Xn};
solutions Y ={Y1, ...,Ym}; M(C) - matrix of compliance specifying model relationships between conditions and decisions.
This interpretation of data reflects the principle of complementarity, according to which conditions are provided in which there is a continuous change in the behavior of objects in the conflict environment. The formal model of information transformation opens up the possibility of finding solutions using hierarchical structures that are characteristic of the tasks under study.
and is a universal tool for analyzing and finding solutions.
Thus, the CAS is considered as an active system functioning in a complex dynamic environment of interacting objects. Management of MTC is to establish the procedures, minimizing an objective function that ensure the maximum effectiveness of management in the current situation. Active elements are defined as CAS objects whose functions are aimed at modeling and visualizing the dynamics of a conflict environment within the framework of the UCS concept . When generating alternatives and developing control actions, a collective strategy is selected, taking into account the strategy of the active elements of the system. The hypothesis of independent behavior of active elements of the CPU is considered within the framework of the paradigm of information processing in a multiprocessor computing environment. The synthesis of an optimal control function for active elements of the CPU ensures maximum efficiency of information processing procedures. The set of implemented actions is determined by the set of PPR procedures. Planning actions when assessing the state of the CO and predicting its development consists in choosing effective planning procedures based on optimal criteria
The task of modeling CO dynamics is to construct scenarios (situation models) with a dynamically changing class of strategies and manage the scenario. To solve the problem, a scenario SC is formed, the execution procedures of which consist in representing SC as a combination of strategies (alternatives) Sctj and control moments tj, (j=1,...,N)
. =
mapping the set of effective strategies as two sets, the first of which corresponds to the set of arcs, and the second to the set of benefits of these strategies in the set of arcs.
The crucial rule for choosing alternatives in the multi criteria optimization problem is represented by the intersection of fuzzy goals Gi and constraints Cj or a convex combination taking into account their relative importance: (20) = 1 ∩ … ∩ ∩ 1 ∩ … ∩ … ; = ∑ + ∑ , ∑ + ∑ = 1, where α is the importance coefficient. (21)
In accordance with the concept of dynamic catastrophe theory on the basis of a supercomputer complex CAS a strategy for interpreting the evolution of the CO is implemented as the ability to transform a set of input signals into a set of output signals in the form of a formal model:
(Attr) = ⟨ (Stab), (Cap)⟩, (22) where G(Attr) - attractor sets, displaying a model of interaction in a hostile environment Oh; G(Stab) - many, forming a movement CO to the target attractor; G(Cap) set, characterizing the behavior of the CO in the loss of stability of the environment.
The CAS computing complex implements the inputoutput operator behavior functions and provides solutions to identification, approximation, and prediction problems that determine the behavior of the CO in the process of evolution. The interaction space within the framework of dynamic catastrophe theory defines the interpretation and control functions, which are used to carry out operational control of the characteristics of an aggressive environment in the course of evolution (Fig. 3).
Iterative process of information transform in the implementation of the dynamic theory of catastrophes
where Фj{f(•)| µ}, (j=1,..., 5) - functions that define classes of interpretation models: Ф1{f(•)|µ} and Ф2{f(•)|µ} computational and diagnostic models; Ф3{f(•)|µ} - models defining the strategy of dynamic catastrophe theory; Ф4{f(•)|µ} - models for analyzing and predicting the current situation; Ф5{f(•)|µ} - models of a dynamic knowledge base.
The construction of the control function at each step of the iterative procedure is based on the synergetic paradigm π(S) in the form of a sequence of actions: π (S ) = f j (•) ∆t1 ,, f n (•) ∆tn , (24) where fj(•) is the control law defining the expansion and contraction phases depending on the state interpretation function at the j-th stage of the system evolution (j=1,...,n); ∆tj is the duration of the stages.
functions is carried out when modeling the behavior of an
model is constructed using MAC and neuro-dynamic
systems (ND-systems) oriented to parallel processing of
information in a supercomputer environment of the CAS
[
MODELING OF BEHAVIOR IN CONFLICT SITUATIONS
The theory of strategic decisions in managing CO behavior provides for a transition from situational management to management with modeling. Relationships in graph-based interpretation of network models allow us to take into account the consequences of decisions being made and control the behavior of the CO not at the level of actions, but at the level of chains of events. To perform simulation procedures in the created virtual space, abstract symbols of various classes of elements of the structure of an aggressive environment are formed and the ability to interpret its behavior within the framework of the theory of synergetic control is formed.
The facts and phenomena of CO modeling are related
to various interpretations of activity in solving behavior
training tasks using simulations of the physiological and
mental functions of objects in a conflict situation. The
functions of sensory systems are implemented in the
construction of algorithms for information processing
based on the concentration of "consciousness" on the most
important aspects of the development of the interaction
process, which reflects the evolution of the conflict
environment within the framework of a dynamic model of
catastrophes (Fig.5) [
The concept of a training model as a mechanism for coordinating the activity of interaction processes of conflict objects and the overall balance of information processing procedures of a supercomputer CAS ensures the fulfillment of the main modeling. It's task is to create a computing environment for virtual modeling of information-physical processes that run in parallel and ensure the organization of information exchange between processes (synchronization), and also decision support in a complex dynamic environment. The controlling influence that changes the state of the CO in accordance with a given law is described using the relations: 0( ( )0),..., ( ( ) ). (25)
Here y(Λ(π)) −(π) is a vector of parameters (π0,...πk) that define the characteristics of the environment and perturbing influences for a given CO evolution in accordance with the operating modes of the CPU within the permissible "input - output" region.
CAS software complex based on the dynamic theory of catastrophes. The conceptual model of assessing the adequacy of mathematical models describing the system of interaction of objects in conflict situations formalizes the processes of constructing problems and criteria functions for interpreting the evolution of the CO in the implementation interval. For rice.6 presents a sequence of information processing operations that determines the criteria basis for evaluating the adequacy of mathematical description of interaction processes in conflict situations.
CONCEPTUAL MODEL FOR ASSESSING THE ADEQUACY OF FUNCTIONING OF THE INTERACTION SYSTEM OF CONFLICT ENVIRONMENTAL OBJECTS
computational technology for determining the parameters of an aggressive environment, dynamics of interaction of environmental objects, as well as the stages of evolution in predicting the behavior of elements of the modeled system are highlighted.
The strategy for assessing the adequacy of UCS
procedures in the functioning of the computing complex
(figure 7) defines the formalization of the conflict situation
based on the factors that characterize a priori information,
the concept of the minimum description length (M DL),
and the problem of complexity. Here the sequence of
stages of forming an adequate UCS model within the
framework of the MDL concept [
is solved by integrating a priori information, the concept
of MDL and the problem of complexity, which determines
the choice of a solution in accordance with the conceptual
model of dynamic catastrophe theory [
modified scheme of O. Balchi [
Neural fuzzy modeling
Neuro Evolutionary modeling 4 Generation and analysis of alternatives
Computational experiment Generation and analysis of alternatives 4 Assessment of adequacy
Construction of NF, NE models Using a physical experiment Selection and analysis of the preferred model 3 3 3 Computational experiment 4
Hypotheses and simplifying assumptions using 2 Assessment of adequacy
Version M 2
Parametric synthesis Structural synthesis Version S Version P Analysis of
results Physics experiment 1 1 1 5 5 5 Model research
Assessment of adequacy
Model construct 4 Model analysis 5 5 5 Space of alternatives Choosing a solution 4 Assessment of adequacy Using a physical experiment Selection and analysis of the preferred model 3 3 3 Using hypotheses and simplifying assumptions 1 1 1
Version M 2
Correlation analysis Analysis of variance 2 2
Version S
Model selection Formation of an ensemble of models Version P Simplifying assumptions Hypothesis formulation
2
Selection of NF, NE models Improving the model 4 Bank analysis of ND-models Assessment of adequacy
The first cycle is associated with the development of competing models (modeling- M), implemented on the basis of the ND-system and methods of classical mathematics. In the course of this cycle, the structural and parametric synthesis of the neural network is implemented in the tasks of neuro-fuzzy NF and neuro-evolutionary modeling, and for the competing model, the assessment of the overall structure and components within the framework of sequential statistical analysis procedures.
appropriate mathematical (simulation) experiments
performed with competing models (simulation- S) for
given initial conditions and input vector elements. Here
NF and NE models of data Bank analysis are formed, on
the basis of which a computational experiment is
implemented, generation and analysis of alternatives and
assessment of adequacy. Construction and analysis of the
competing model is carried out in accordance with the
formalization of the problem in conditions of significant
uncertainty in accordance with the algorithm [
conducting physical (physical- P) experiments, on the basis of which models are formed that provide an assessment of adequacy under conditions of complete uncertainty. During ND this cycle, the components of the
Intelligent support for M,S,P procedures is provided by
the calculation management system and visualization of
modeling results. As estimates of the adequacy of fuzzy,
neural network and competing models, we should adhere
to the recommendations that determine the use of UCM
procedures in complex dynamic environments [
Thus, the development of the CAS software package and demonstration of its functionality in various conditions of interaction of objects in a conflict environment is carried out on the basis of supercomputer technologies for modeling and visualizing interaction situations using multi-mode ADS. In order to achieve this goal, the following main tasks are envisaged: ˗ formation of a scientific and technological Foundation for the dynamics of the CAS functioning in UCS mode on the basis of supercomputer technologies for modeling and visualizing interaction processes using the results of fundamental and applied research; ˗ ˗ solving qualitatively new problems in terms of volume and complexity of conflict situations interpretation in order to increase the effectiveness of management decisions to ensure the safety of critical facilities; ensuring the integration and effectiveness of research and development, creation and practical application of a modern set of applied tools for analyzing and predicting the development of targeted organized antagonistic conflicts in conditions of uncertainty based on CAS and high-performance information processing tools.
The solution to these problems will achieve the goal of creating MTC - improving the efficiency of FFD-based simulation and visualization of the dynamics of interaction between the elements of the conflict environment on the basis of supercomputer technologies. The conceptual solutions that define the problem of connectivity, complexity and stability based on the UCS concept are aimed at ensuring the principle of adaptability and reflect a single trend - an adequate description of the hierarchical organization and the identification of significant functionally significant elements of interaction in a conflict situation. The above analysis is crucial in the search for mechanisms that ensure the formation of collective properties of interpretation of an aggressive dynamic environment, leading to the formation of hierarchical systems and the emergence of the possibility of their mutual modeling. Compression of the mathematical description of conflict situations is a necessary prerequisite for the formation of collective properties of interaction models in UCS through the organization of cross-correlations between the corresponding variables.