An analysis of a complex man-made hierarchical structure with an automated control and document management system is carried out in the conditions of active information and resource attacks, using the category algebra, which allows detecting attacks on a dynamic system, determining the risk levels of emergency situations and creating appropriate countermeasures. For the first time, the methodology of constructing categorical models for the representation of a dynamic hierarchical structure in the space of states is substantiated and developed, diagrams of energy-active objects of a dynamic system are provided, taking into account the effect of resource and information attacks on it, and methods of decision-making in emergency situations using risk assessment. For the first time, a structural diagram of the balance of the game between threats and control in the system is formed, taking into account the factors of threats and their influence on the objects of the system, on the basis of which a functional diagram of the information-resource hierarchy of the aggregated system control in the mode of countering threats is proposed. For the first time, the categorical diagram of an information attack is substantiated and the systemology of the formation of the object structure and the assessment of the dynamic state under resource threats and information attacks is proposed. As a result of the research, a hierarchical structure of the control system of the technological complex is formed under the risk of emergency situations, with the selection of security features of the document flow in the formation of control decisions at the techno-aggregate, operational administrative and strategic levels, which allows the use of the proposed methodology in the conditions of decision-making support during the functioning of complex hierarchical control systems.
The structure of the hierarchical man-made control system has a complex organization, so it is not an easy task to cover all aspects of its functioning, to present and identify energyinformation connections. The problem is especially complicated if the dynamic system is affected by negative factors in the form of information and resource attacks, which can lead to uncontrolled changes in the state of aggregates and objects in the technological cycle of system control. In addition, the action of information and infrastructure attacks of an aggressive type can lead to the destruction of hierarchical connections and the system structure, which, in turn, threatens the emergence of emergency situations with a high level of accident risk. These problems are not fully solved both in the classical control theory and in modern approaches based on system analysis. Only the use of the category algebra by constructing diagrams of the structure of connections and determining the cores of influence on the system space of states allows detecting attacks on a dynamic system and creating means of countering possible attacks.
To achieve the goal of scientific research, it is necessary to solve the following tasks: • • • • to justify the use of the category algebra methods for solving the problems of constructing the structures of hierarchical dynamic systems with complex connections and under external negative influences; to construct categorical structural diagrams of transformations in an energy-active system under the threats, in the space of states and dynamics in time of a complex system; to propose a categorical representation of the model of threats to the system and to develop a structural diagram of the game between threats and control in the system; to develop a functional scheme of information-resource countermeasures against threats in the hierarchy of the man-made system and the hierarchical structure of the control system of the technological complex at risk.
The analysis of the problem of emergency and risk situations under the influence of active
threats and attacks has shown the importance of building models for detecting attacks by the
way they affect system objects. The textbook of domestic scientists [
The concept of smart manufacturing and its impact on the future automation of labor with
decision-making technology is proposed in [
The scientific article [
Modern developed methods for analyzing general industrial control systems for hierarchical technogenic structures are presented in [13, 14]. Work [15] consider applied decision support systems based on risk analysis of complex systems.
Paper [16] presents the use of an object-oriented Bayesian network for scenario risk assessment. A model of probabilistic coverage of key factors affecting accidents in fragmented structures is developed. The study in [17] proposes a model-based methodology for hybrid management of risk assessment of reliability, availability, maintainability, and safety for critical systems. The result is a method for analyzing cybersecurity risks for industrial control systems. Agrawal et al. [18] defined an ontology to represent ISO/IEC 27,005, 2018 standards to provide a step-by-step understanding of the meaning of security concepts and their interrelationships. Researchers such as Blanco et al. [19] reviewed 31 security ontologies. Both studies group security ontologies into three categories: general, specific, and theoretical.
Two popular risk assessment methods tested for the nuclear industry use probabilistic risk assessment [20, 21], while others use dynamic Bayesian networks [22, 23]. The human factor and reliability in risk assessment and management in the context of threats and attacks are considered in the scientific paper [24]. Paper [25] presents a model of a dynamic and iterative process in which experts discuss a multi-criteria decision-making problem in complex management structures. The considered methods of modeling fuzzy preferences are aimed at evaluating, comparing, selecting, prioritizing and/or organizing alternatives.
Let one construct the structure of the hierarchical system in a categorical form. To do this,
its main elements and parameters should be defined: [
⊂ is the set of values of control actions on the mdimensional vector space; Y is the set of values of input parameters on 0; X is the space of states on 0; Ω is the space of input actions for which : → , ∈ Ω; Г is the space of output parameters Г: → ; α is the display of the transition when the system status changes α: (
× × × Ω) → .
For the moment of each transition one has: ( + 1, , , ) ⟼ ( + 1, , , ) = ( ) + ( ), (1) where , are matrices ( × ), ( × ) over K; is the output representation × → for which ( , ) ⟼ ( , ) = ( ) is true.
To study the dynamics of the system for each component, it is necessary to identify the model (input-output function) as a transfer function that connects the initial state of the system ( ) with the input control signal ( , ) through the parametric-time operator ( , ): ( , ) → ( , + ∆ ).
For linear systems in the classical theory, the "input-output" representation function is
associated with the concept of the transfer function [
If there is some homomorphism for the transfer function in the structure of dynamic systems then it can be represented in the form: ( ) = ∑ =1 ( ), where ( ) describes
If there is a factorization for which is described by a commutative diagram [
(Fig. 1).
The implementation of the matrix transfer function for an object with interconnected technological aggregates, with a common space of states 〈 = 11, 12, … , 〉 in a dynamic system has the form: = × { }, ( ) = : ( × × × Ω), Ω: { : → }/
Let one construct a diagram for an energy-active object of a dynamic system, taking into account the channels of action of active threats (Fig. 2). → ) are functions of energy transformations; ( → ) are kinetic and, accordingly, electromagnetic operators of energy transformations; IMS are information and measurement systems.
The channels of resource and information attacks ( , ) have a complex structure and their representations, methods of influencing the system and the identification require a systematic and categorical approach.
The decomposition procedure will be carried out for a complex dynamic system IIS with a hierarchical structure into subsystems, blocks and aggregates: =1,
〈 〉 → | =1, =1 → | == 1,1 | =1, → { }.
(2)
Accordingly, a scheme of internal and external connections of aggregate and hierarchical subsystems is obtained when resource and information flows are transformed (Fig. 3).
Procedures for forming the structure of the object are constructed using data and knowledge processing processes in accordance with the problem based on the concept of systemology and categories. From the structure of the man-made system, the basic structures are singled out that describe and show the functions, targets and dynamics of the object according to the specific target task it performs { }.
To achieve the target task in the system, the basic functional structure of the control object is selected, which at its level ensures the achievement of the target: { +3} +2| +2| | = 1, , (4) due to the decomposition procedure of the system into aggregates { +2} .
To get further information about the functional structure of the technological object and the control process, the aggregates are decomposed into components with selected and predefined spaces of states, targets, modes and parameters in Fig. 4.
Designations in Fig. 3, 4: ( , , ) are dynamic characteristics of the function; ( , , ) are class models of process trajectories at the input and output of the system; ( , , ) is the division of the space of states into alternatives; ( , , ) are areas in the space of targets, mode, state of the object and system; (П , П , П ) are spaces of states, targets, the initial parameter Y; ( П , П ) are situations in the space of targets and states according to ( ).
On the basis of the given description of the categorical structure of the system in the terminal time base and the system structure of dynamics, a categorical representation of the action model of active threats to the system (informational and resource) is developed (Fig. 5).
Designations in Fig. 5: is a generator of the trend of changes in the constant component of the reliability of aggregates; ( ) is a generator of impulse discrete active influence on the object of the structure of the document management system, is a targets.
To assess the parameters of the system dynamics, under the control action and the influence of threats, a parametric-temporal representation of the behavior of structure objects in the spaces of input parameters, control, the mode of the object according to the load and changing its trajectory is used based on the analysis of the interaction balance <control ↔ threats> (Fig. 6), that is, the system information-resource game.
The following main systems in the structure of the game are highlighted: a man-made aggregated system with control hierarchy; a system of external influence with a subsystem of active attacks complex of interrelated factors of influence on the aggregate sub-structure, as well as which forms a information and management, strategic one.
Based on the game concept, a functional scheme of active countermeasures against threats and attacks is developed (Fig. 7). hierarchy of a man-made system
The designations in Fig 7: { } are factors of external influence; is an information attack; SAC is a system of automated control of aggregated sub-structure { | =1}IMS is an information measuring system; П ( , , ) is a flow of technological and energy resources; П( ), П( ) re spaces of states and the system targets; ( ) is a coordination of targets in the mode of threats; ( , ) are data and knowledge bases of automated document management system, ( ) is an activator of attacks.
According to the functional scheme
of the information-resource hierarchy, the substructure ( ) of the attack initiation system is considered, which includes: ( ) attack resources; an initiator of attacks;
the target task of the attack; a complex formation of threat factors, which reflect the activation process and the action of influencing factors on the system control.
In accordance with the strategy of the information-resource game, a categorical diagram of the attack on the ACS is constructed (Fig. 8).
Designations in Fig 8: is an attack activator; is a generator of a random process ( , ); is an energy attack resource; is an information attack resource; is a component modulator; ( ) is a generator of active action; ( ) is a generator of target task of an active threat, attack; ⊗ ( ) is a component shaper of the factor (of the information-resource class); ( ⁄ ) is an activator of the factor action on the system; is a channel of influence on the ACS system.
To obtain the control situational information about the object state, it is necessary to decompose the object into the following components, which ensure the achievement of the local target: { +1}
+1| +1| → .
At the lower level of the object states 〈 +3, +2, +1, 〉the process of identification of elementary structures and knowledge is carried out, which reflect the peculiarities of the complex functioning | =+11,, .
To analyze the general state of the system, taking into account the above, it is not possible to present the information essence of the situation that has developed in the system (Fig. 9).
In Fig. 9, the following information-resource components and procedures are denoted:
•
•
•
•
•
the procedure for identifying a critical situation in the object under external influences
and attacks on the control structure [
The evaluation of the results of the objects and aggregates state can be carried out using
systemology, information technology and intelligent decision-making procedures and rules in the
control process, which ensure the achievement of the target in the mode of the current situation
assessment. The use of systemology methods is used to create a theoretical representation of the
formation of the object structure, to determine the space of its possible states and changes in the
object under the influence of threat factors in the target control process. With the help of the
concepts developed in works [
Common components of a dynamic system with a hierarchical structure include (Fig. 10): • • • aggregates, blocks, energy-active objects that ensure the process of resource transformation into energy and are characterized by the operating mode and dynamics; dynamic characteristics of technological processes at all stages of functioning (power, mode: limit - standard); information control procedures and algorithms for describing situations, data flows in the control process.
Resource, information, control, dynamic processes, channels of flows transfer and exchange cannot be isolated using classical technologies of synthesis and analysis of systems, which in turn complicates the process of identifying crisis nodes and channels through which the redistribution of resources, energy, data flows and control teams occurs. That is, with the help of classical methods and technologies, in the structure of a man-made system it is impossible to single out agents of influence on the way the system functions, the most vulnerable places of attacks on the control process and system goals, therefore it is impossible to describe the control process using game models. To solve the problem, the concepts of targetoriented systemology of constructing the structure of the object and assessing the dynamic state are developed as a basis for forming a strategy of active game against threats (Fig. 10). under resource threats and information attacks
The designations in Fig. 10: IA an intelligent agent; Fci a target activation factor; DKMS a database and knowledge management system; ILSSP an intelligent logic synthesis system processor; ( (
⁄ ) ) a unit for processing the system situation in the control object ( ) at the moment of time t in the interval ; a criterion of quality requirements; ̂ current quality; reference quality; : ̂
≥ the synthesis product to the target task; ∗ a factor of influence activation on the system. ⇒ [ (
) ↔ ( )] compliance of a quality criterion in the system dynamics process;
Based on the systemology of the formation of the structure of the man-made system, a model of the hierarchy of the control process and the channels of transfer of threats and attacks is developed, which includes the following levels (Fig. 10): 1 - models of the manmade process (active, thermodynamic, physical); 2 - the level of automatic control; 3 - the level of operational control; 4 - the level of threats to the control; 5 - the level of threats to the target orientation of the control system; 6 - the level of information assessment of the dynamic situation in the system; 7 - a mathematical apparatus for analyzing the structure and the system dynamics under threats in the target control process; 8 - the level of formation of the target control task in the conditions of threats; 9 - the level of processing of situational information under threats (USP - a unit of signals processing); 10 - the level of the model of the process of solving a problematic situational problem; 11 - the level of project formation of the defense system against attacks and threats.
Based on the system method of forming the security system structure, a hierarchical structure of the man-made complex control system under threats is constructed (Fig. 11).
In the man-made hierarchy (production, transport, organizational-administrative control units, printing industry, media), the formation of the structure of the security system is based on systemology and methods of target-oriented decision-making to solve the problems of crisis situations.
Let me emphasize the security features of document circulation when formulating control decisions at the techno-aggregate, operational, administrative, and strategic levels (Fig. 11): 1 - a technological structure, which is provided by normative and regulatory documents; 2 - documents of current control and data storage from information and measurement systems; 3 - operational control documents and mode maps and reports for ACS-TP; 4 - documents and reports in the operational-administrative control system; 5 - documents that determine the strategic control of the man-made complex; 6 -documents of the strategic level for forecasting the situation and target orientation of the man-made complex;
⁄ - the core of controlling data exchange processes; DS - diagnostic system for ACSTP; MT - management team; DM - decision-making; - information threats.
To develop systems for the protection of the strategic structure and the design process, it is necessary to take into account the peculiarities of data accounting between all levels, which are the basis for the formation of documents (correction, management, coordination, target orientation, assessment of situations in the system), which determines the appropriate protection measures.
A methodology for constructing categorical representations of models, structures, components, and systems, which is necessary for detecting the coordinates of intrusion attacks, is proposed, and a generalized representation of structures in a hierarchical system in the category algebra is substantiated. This makes it possible to detect vulnerabilities and threats that lead to information and resource attacks, and as a result - emergency situations in the process of functioning and control of complex hierarchical systems.
When assessing the parameters of the system dynamics, in the process of controlling hierarchical structures and the influence of active threats, a parametric-temporal representation of the behavior of the structure objects in the spaces of input parameters, control, mode of the object according to the load and change of its trajectory is used. Based on the analysis of the interaction balance <control ↔ threats> in the form of a system information-resource game and the study of the functioning of the hierarchical system on a certain terminal cycle, it is found that the game model coincides with the real processes of man-made system control under threats. Based on this, a structural diagram of the balance between threats and control in the system is developed and substantiated, an aggregate diagram of a hierarchical system with internal connections is constructed to identify the cores of attacks on it, which can be used in the context of decision-making support.
A method of structuring man-made systems is developed based on the assessment of the dynamics of changes in the state of objects to identify critical situations in the form of attacks and negative disturbances on the control process and structural organization of man-made systems. It is shown that the risks of accidents are determined on the basis of the assessment of changes in the state of objects relative to standards, specified limits and normative modes of the system functioning in the conditions of transition of the trajectory of the state through the limit line of the functioning mode of the energy-active object.
The general concept of this approach can be applied to any company and man-made structure with a hierarchical control structure. Quantitative estimates of losses obtained according to the analysis of possible threats and vulnerabilities are submitted to the input of the model, for example, organizational assets, cognitive characteristics of factors affecting the man-made structure, taking into account risk coefficients, characteristics of various control risk components and linguistic considerations of experts in the field of security and system control and decision-making. Risks of production losses are formed in the terminal production cycle and can also be changed under the influence of active threats in the production and control process. It is necessary to take into account all the threats and vulnerabilities of such man-made hierarchical systems, and only then it is possible to determine a comprehensive indicator of the risk of system failure under the influence of active threats.
The paper solves the scientific and applied task of developing a methodology for constructing a model of the structure of hierarchical control systems of complex man-made objects under threats and attacks based on the use of the category algebra. The possibility of constructing procedures for the structuring of man-made systems (current and at the design stage) is substantiated based on the use of system analysis and the theory of categories.
The scientific novelty of the study is as follows: 1. for the first time, categorical structural diagrams of transformations in an energyactive system under threats, in the space of states and dynamics in time of a complex system are developed; 2. the categorical representation of the model of the effect of threats on the system is improved and a structural diagram of the game between threats and the control process in the hierarchical system is developed; 3. for the first time, a functional scheme of information-resource countermeasures against threats in the hierarchy of man-made systems is developed; 4. for the first time, the hierarchical structure of a technological complex control system is developed under risk conditions; 5. the proposed categorical representations for assessing the risk of failure of the control system and document flow are tested and verified as part of a hierarchical production system for the example of risk assessment of printing productions, and also a systemcategory diagram of interaction is proposed as a training in the information-resource game <control ↔ threats>.
The practical significance of the obtained results is that the proposed method of determining the coordinates of attacks based on changes in the state of objects in a dynamic hierarchical system allows determining the risk of emergency situations, which has been tested in the control and document management system as part of the hierarchical system of printing production and can be used in various man-made hierarchical systems when solving control decision-making tasks, designing and improving protection systems.
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