=Paper=
{{Paper
|id=Vol-3675/paper18
|storemode=property
|title=Decision-making logic in operational emergency situations for hierarchical systems management
|pdfUrl=https://ceur-ws.org/Vol-3675/paper18.pdf
|volume=Vol-3675
|authors=Liubomyr Sikora,Nataliia Lysa,Olga Fedevych,Yurii Lysyi
|dblpUrl=https://dblp.org/rec/conf/intelitsis/SikoraLFL24
}}
==Decision-making logic in operational emergency situations for hierarchical systems management==
https://ceur-ws.org/Vol-3675/paper18.pdf
Decision-making logic in operational emergency
situations for hierarchical systems management⋆
Liubomyr Sikora1,†, Nataliia Lysa1,∗,† , Olga Fedevych1,† and Yurii Lysyi2,†
1 Lviv Polytechnic National University, 28a Bandery Str., Lviv, 79000, Ukraine
2 Ukrainian Academy of Printing, 19 Pid Goloskom Str., Lviv, 79000, Ukraine
Abstract
The article considers the mathematical and systematic apparatus for describing structures with
subsystems and systems with decomposition with the corresponding functional links in the form of
operators.
In the analysis of literature sources, it is substantiated that the problem of managing complex systems
is not fully solved under the influence of structural, informational, psychological threats, and the
problem of structuring the system as a basis for the formation of targeted decisions by operational
personnel under active threats is relevant in the future.
The mathematical and systematic apparatus for describing structures with a set of relevant
interconnected components is presented. The functional blocks of the system with the corresponding
functions and characteristics such as functional transformations, cascade connection in the
technological structure, models of adaptive and multiplicative interaction, systems with feedback and
hybrid connections and mathematical operations are presented.
A method for risk assessment in management decision-making in hierarchical systems under extreme
conditions, taking into account the cognitive components of operators, has been developed.
Keywords
emergency situation, system, management, logic, risk assessment 1
1. Introduction
Systems analysis arose as a result of attempts to apply the methods and tools of systems theory
to solve problems of managing complex hierarchical systems in normal and emergency modes.
With the development of man-made structures, information barriers arose, which formed
complex management tasks [1, 24]:
• increased bandwidth of data transmission channels and rapid growth of their
heterogeneity and blurring;
IntelITSIS’2024: 5th International Workshop on Intelligent Information Technologies and Systems of Information
Security, March 28, 2024, Khmelnytskyi, Ukraine
∗ Corresponding author.
† These authors contributed equally.
lssikora@gmail.com (L. Sikora); lysa.nataly@gmail.com (N.Lysa); olha.y.fedevych@lpnu.ua (O. Fedevych),
llusuy@gmail.com (Y.Lysyi)
0000-0002-7446-1980 (L. Sikora); 0000-0001-5513-9614 (N.Lysa); 0000-0002-8170-3001 (O.Fedevych); 0009-0000-
1734-2814 (Y. Lysyi)
© 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
• the complexity of the problems to be solved exceeded the ability to process data flows
by humans and the processor of the automated control system (technologic process).
This led to the creation of information systems (as a tool for improving the validity and
efficiency of decision-making management) and information technologies for synthesizing
strategies for achieving goals, tactics, and system planning of actions at the facility.
In the process of solving complex problems, there are the following levels of hierarchies [1]:
• the hierarchy of the lower level of the object's structure in terms of modules and units;
• hierarchy of the n-th order control structure depending on the target orientation and
the level of information processing (sensors, processing units, image formers of dynamic
situations);
• hierarchy of the decision tree and division of the target space into clusters.
• hierarchy of priorities in the procedures for ranking alternatives in the target space.
• hierarchy in the construction of sets of goal trees and corresponding classes of strategies
and evaluation of their effectiveness relative to the reference way of goal realization.
At this point, this work will investigate some aspects of mathematical and logical basis for
hierarchical systems management.
2. References analysis
Books [2, 21] substantiate the problem of integrating methods of situational analysis and causal
diagrams of the impact of factors on the management process.
Work [3] consider the problems of management quality and methods of risk assessment in
information and control systems.
Books [4, 5, 23] consider logical and cognitive methods and their use in the process of
training operational management personnel for all levels of the hierarchy of integrated
management of production structures, and substantiate their effectiveness.
Works [17, 18, 22] consider the problem of improving the quality of control processes in
complex systems with a hierarchical structure, intellectualization of situation control,
knowledge features of decision-making, synthesis of robust control strategies, cognitive
features of the ACS operator's thinking process, complex models of energy-active facilities
management in the face of threats and information attacks.
Monograph and work [6, 7, 14] substantiate information and logic-cognitive technologies
for the implementation of control processes in the face of active threats and terminal
emergencies.
Works [8, 9, 13] consider the problem of cybersecurity based on logical and cognitive
methods, information and intelligent technologies for processing data flows and event scenarios
in infrastructure, taking into account the level of risks using categorical models for representing
the organization of complex man-made industries.
In [10] substantiate information technologies for developing methods to ensure the cognitive
stability of operational management processes for personnel at all levels of the hierarchy of
complex systems.
Works [11, 16] considers the categorical models of representation of the complex systems
structure and their effectiveness in forming strategies in infrastructure in case of internal and
external conflicts.
In [12], information technologies for identifying the structure of systems, cognitive methods
for assessing situations when factors affect the management process and increasing
sustainability are developed.
Works [15, 19, 20] substantiate the influence of the cognitive characteristics of operational
personnel in the implementation of management in extreme situations, assessing the level of
threats at the terminal intervals of formation and decision-making for targeted management,
and risk assessment in case of errors in strategic decisions.
3. Main research description and results
Important in the procedure for finding a way to solve problems is the acquisition of data and a
model for identifying knowledge in an active diagnostic and expert mode, identifying their
logical and cognitive structure [1].
The next step is to isolate the control object from the environment of the technogenic
system, and define its boundaries, functional and information structure [1], build a formalized
model, assess its adequacy, identify limit and emergency modes and, accordingly, observability
and controllability.
The responsible procedure is the object aggregation scheme and the construction of a
mathematical model of the hierarchy of the resource and information components of the system
in the form of a scheme for structuring relations (linkage matrix, graphs, Petri nets) [1], the
Saaty model, and the n-level model for assessing local and global priorities.
At the same time, there are hierarchies of the forward and reverse process [1]:
Table 1
Hierarchies of the forward and reverse process
A direct process of planning the future Reverse process as a management program
Macro objectives Desired scenarios for achieving the goal
Factors Problems and the possibility of realizing
local goals
The strength of the factors Operators and teams
Operators Team goals
Operator's goal Team policy
Team policy Team strategy in the goal achievement
program
Contrasting scenarios -
Generalized scenario of events leading to -
the required result
The course of events and the system's Action plan to achieve the goal and its
implementation of the trajectory implementation
towards the goal
The next stage is the hierarchy of procedures for streamlining the stages of action planning
and structuring the management system in accordance with the global goal [2,8].
The following stages are carried out in accordance with the global goal [2,9]:
• systematic analysis of the problem and its formalization, identification of critical zones
in the space of goals and states of the object;
• decomposition of the problem and construction of scenarios of possible events;
• selection of means to achieve the goal, both local and global, and appropriate scaling of
the goal space for its structuring;
• methods and models for assessing the situation in the system as the main means of
identifying the information structure of processes in the system and the logic of
decision-making;
• identification of logical contradictions in the processes of decision-making and
assessment of dynamic situations;
• taking into account causal relationships in the scenario of events and building categories
as a way to display information structures;
• building strategies for coordinating team actions and assessing the level of their
interaction under risk;
• analysis of the degree of coordination of their actions in the context of the
implementation of the action plan and ways to resolve conflicts at all levels of the
integrated hierarchical automated control system (IHACS);
• development of coordination strategies based on the information and regulatory
framework and construction of appropriate algorithms, with justification of their logical
structure.
In accordance with the current situation, let’s describe hierarchical structures as an
organization for the implementation of targeted tasks, taking into account active attacks and
threats and the cognitive component of the operator.
3.1. Mathematical and systematic apparatus for describing structures
Definition. A subsystem S ′ of a system S will be any subset of S ′ ⊂ X × Y, and an element of
systems will be a set of appropriately connected components by which the systemS S =
(S1 … Sn ) can be restored.
Definition. Definition. A decomposition of a system S is a set of (S1 , S2 , … Sn ), for which S =
(S1 + S2 +. . . +Sn ) and X = (X1 × X 2 ×. . .× X n ), Y = (Y1 × Y2 ×. . .× Yn ), are components of
the system.
Functional relationships in the system are described in the form of operators.
3.1.1. The system components connections design operator
For two given systems S1 ⊂ X1 × Y1 and S2 ⊂ X 2 × Y2 , a design operator is introduced defining
the structure similarity class, whose representation is as follows:
Π𝑟𝑟1 : (𝑋𝑋1 × 𝑋𝑋2 ) × (𝑌𝑌1 × 𝑌𝑌2 ) → (𝑋𝑋1 × 𝑌𝑌1 ), (1)
Π𝑟𝑟2 : (𝑋𝑋1 × 𝑋𝑋2 ) × (𝑌𝑌1 × 𝑌𝑌2 ) → (𝑋𝑋2 × 𝑌𝑌2 )
Accordingly then it is possible to carry out an independent decomposition 𝑆𝑆 into two
subsystems of unrelated type:
𝑆𝑆 ⊂ (𝑋𝑋1 × 𝑋𝑋2 ) × (𝑌𝑌1 × 𝑌𝑌2 ),
𝑆𝑆1 = Π𝑟𝑟1 (𝑆𝑆) 𝑎𝑎𝑎𝑎𝑎𝑎 𝑆𝑆2 = Π𝑟𝑟2 (𝑆𝑆),
Π𝑟𝑟1 : (𝑋𝑋1 , 𝑋𝑋2 , 𝑌𝑌1 , 𝑌𝑌2 ) = (𝑋𝑋1 × 𝑌𝑌1 ), (2)
Π𝑟𝑟2 : (𝑋𝑋1 , 𝑋𝑋2 , 𝑌𝑌1 , 𝑌𝑌2 ) → (𝑋𝑋2 × 𝑌𝑌2 ).
with state spaces, control objects (𝑂𝑂𝑈𝑈𝑖𝑖 ), control systems (𝑆𝑆𝑈𝑈𝑖𝑖 ), information structures (𝐼𝐼𝑆𝑆𝑖𝑖 ),
and mode parameters (𝑌𝑌𝑖𝑖 ).
Figure 1: Connections design operator.
3.1.2. The operator of systems cascade decomposition and their functional
organizations
The decomposition procedure is the basis for the allocation of functional blocks with
appropriate characteristics and functions.
П1 – functional transformations 𝑓𝑓 ∶ 𝑋𝑋 → 𝑌𝑌 that define resource, technological, and
measurement transformations, executive team actions, and one-step operations.
П2 – cascade connection in the technological unit structure, information and measurement
→ Y1 →
operations
S1 : X1
(
→ S 2 : У1* ⊕ У *2 ) }SitПi
П3 – model of additive and multiplicative interaction in the course of technological and
information operations:
(𝑋𝑋1 , 𝑋𝑋2 ) → (𝑆𝑆𝑖𝑖 ) → 𝑌𝑌𝑖𝑖
𝑆𝑆𝑖𝑖 : (𝑋𝑋1 ⨂𝑋𝑋2 ) → 𝑌𝑌𝑖𝑖 (3)
𝑆𝑆𝑖𝑖 : (𝑋𝑋1 ⨁𝑋𝑋2 ) → 𝑌𝑌𝑖𝑖
П 4 – system structure with feedback (information, control).
П 5 – a combination of structural components with hybrid feedback.
П 6 – blocks for performing mathematical operations in information and management
subsystems.
Any system 𝑆𝑆 ⊂ 𝑋𝑋 × 𝑌𝑌 allows decomposition in the form of a cascade structure if the
conditions [5, 6] for the functions are met.
The decomposition of the system infrastructure provides an appropriate representation for
displaying technological processes, information and control operations, and representation of
threat factors and information attacks.
In accordance with the structures, let’s distinguish functional operational elements (Fig. 2):
1. Transformation of material and energy resources (units, power units) into a product
(𝑀𝑀𝑅𝑅 → 𝐴𝐴𝑇𝑇 (𝑀𝑀𝑅𝑅 ) → 𝑃𝑃𝑅𝑅𝑇𝑇 );
2. Transformation of data flows into an information resource based on data processing
operations {𝐷𝐷𝑖𝑖 } → 𝐴𝐴𝐼𝐼 ({𝐷𝐷𝑖𝑖 /𝑇𝑇𝑚𝑚 }) → 𝐼𝐼(𝐷𝐷𝑖𝑖 );
3. Transformation of information resource and data flows into a cognitive knowledge
structure for interpreting the content of the situation
𝑇𝑇𝑖𝑖 𝑇𝑇𝑖𝑖
�{𝐷𝐷𝑖𝑖 }, �𝐼𝐼(𝐷𝐷𝑖𝑖 )�� ⟶ 𝐴𝐴𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 �𝐼𝐼(𝐷𝐷𝑖𝑖 )� ⟶ Sens [Sit(𝑡𝑡, 𝑇𝑇𝑖𝑖 )].
4. Transformation of intellectual and information resource into management actions based
StratU
on goal-oriented strategies Sens [Sit ou (𝑡𝑡𝑡𝑡 , 𝑇𝑇𝑡𝑡 )] ⟶ (𝐶𝐶𝑖𝑖 ) → 𝐷𝐷𝑖𝑖 (𝑈𝑈𝑖𝑖 /𝐶𝐶𝑖𝑖 )
Х1
Y1
(S1 / S2)
Z1
X
Y2
X2
Figure 2: Cascade decomposition operator.
According to the components of the structure, dynamics models are formed.
�(𝑥𝑥, 𝑥𝑥 ′ ) ∈ 𝐸𝐸𝑥𝑥 � ⇔ 𝑆𝑆(𝑥𝑥) = 𝑆𝑆(𝑥𝑥 ′ )
(4)
�(𝑦𝑦, 𝑦𝑦 ′ ) ∈ 𝐸𝐸𝑦𝑦 � ⇔ (𝑦𝑦)𝑆𝑆 = (𝑦𝑦 ′ )𝑆𝑆
with canonical representations of transformations in the form of a chain of information and
control operations:
𝑥𝑥� 𝑦𝑦
𝐸𝐸𝐸𝐸 �𝐸𝐸𝐸𝐸
�𝑥𝑥 → 𝑆𝑆 → 𝑦𝑦� → �𝑥𝑥 → 𝑌𝑌𝑥𝑥 ⟶ 𝑆𝑆 ′ ⟶ 𝑌𝑌𝑦𝑦−1 → 𝑦𝑦� (5)
accordingly, the transformation coordinates of state parameters will be set according to the
control actions:
𝑌𝑌𝑥𝑥 : 𝑋𝑋 → 𝑋𝑋/𝐸𝐸𝐸𝐸
(6)
𝑌𝑌𝑦𝑦 : 𝑌𝑌 → 𝑌𝑌/𝐸𝐸𝐸𝐸
([𝑦𝑦], 𝑦𝑦) ∈ 𝑌𝑌𝑦𝑦−1 ⇔ [𝑦𝑦] = 𝑌𝑌𝑦𝑦 (𝑦𝑦) - determine the transformation of the parameters of the state
spaces of the system S when management actions affect the object and then 𝑈𝑈𝑖𝑖 : 𝑋𝑋𝑖𝑖 (𝑡𝑡𝑖𝑖 ) →
𝑈𝑈𝑖𝑖 �𝑡𝑡𝑖𝑖 + 𝜏𝜏𝑗𝑗 , 𝑈𝑈𝑖𝑖 � ∈ 𝑉𝑉(𝑡𝑡𝑖𝑖 + 𝜏𝜏𝑖𝑖 ) - output state.
3.1.3. Autonomy of functional systems that are part of a hierarchical organization
structure
In the informational sense, decision-making in the autonomous functioning of the system is
achieved by introducing feedback, which provides a logical structure for the decision-making
process. The decision-making logic is based on [1, 2, 7]:
1. detecting the difference between the real and target trajectories in the state space of the
power-active object and control system;
2. assessment of the degree of difference object state trajectories;
3. classification of trajectory differences based on the division of the goal space into
alternative areas (NORMA, ALARM, AVAR);
4. assessment of the situation according to the classification and synthesis of control
actions, according to the strategies for achieving the goal, which ensures access to the
target area of management systems in the face of threats.
Let’s consider some aspects of the systems' functionality.
3.1.4. The concept of complex systems functionality (categorical models of
structures) by Mesarovych
Consider a system 𝑆𝑆 ⊂ (𝑋𝑋 × 𝑍𝑍3 ) × (𝑌𝑌1 × 𝑍𝑍4 ) whose feedback loop link includes the element
𝑆𝑆𝑓𝑓 ⊂ �𝑍𝑍𝑦𝑦 × 𝑍𝑍𝑥𝑥 �. Accordingly, the condition ��𝑋𝑋, 𝑍𝑍𝑥𝑥 , 𝑌𝑌, 𝑍𝑍𝑦𝑦 � ∈ 𝑆𝑆� ⇒ �𝑌𝑌 = 𝑍𝑍𝑦𝑦 �, 𝑍𝑍𝑦𝑦 ∈ 𝑍𝑍𝑦𝑦 ⊂ 𝑌𝑌 is
fulfilled for the system, and the system is defined in (𝑋𝑋 × 𝑍𝑍𝑥𝑥 ) × 𝑌𝑌 space.
The structure of the feedback control system is represented as follows (Fig. 4).
Let’s define additional properties of feedback systems according to [3]:
1. A functional system 𝐹𝐹𝑠𝑠 �𝑆𝑆𝑓𝑓 �: 𝑋𝑋 → 𝑌𝑌 is mutually unambiguous if a number of conditions
are met in terms of structure, goals, strategies:
2. a) the condition of the target functionality (𝐹𝐹𝑐𝑐𝑐𝑐 ): �∃𝑆𝑆𝑓𝑓 : (𝑌𝑌) → 𝑍𝑍𝑥𝑥 � ⇒ �𝑆𝑆𝑓𝑓 𝜗𝜗𝐹𝐹𝑠𝑠 �𝑆𝑆𝑓𝑓 �� -
functionality;
3. b) the functionality of the systems is determined according to the goals ((𝑋𝑋, 𝑍𝑍, 𝑌𝑌) ∈
𝑆𝑆)𝜗𝜗�(𝑋𝑋 ′ , 𝑍𝑍, 𝑌𝑌) ∈ 𝑍𝑍� ⇒ (𝑋𝑋 = 𝑋𝑋 ′ ) - unambiguity.
4. The system 𝑆𝑆 ⊂ (𝑋𝑋1 , 𝑥𝑥 … 𝑥𝑥, 𝑋𝑋𝑛𝑛 ) is functionally controlled if the condition of goals
alignment with the structure and strategies is met:
5. �∀𝑦𝑦 ∈ 𝑌𝑌�(∃𝑥𝑥 ∈ 𝑋𝑋)�(𝑥𝑥, 𝑦𝑦) ∈ 𝑆𝑆� → ∃ �𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆, 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 �𝑈𝑈�𝐶𝐶 ��
𝑖𝑖
6. A multidimensional system will be autonomous as a result of feedback closure only if
the condition of structural and information-management resilience against the impact
of complex threat factors (additive and multiplicative models) is met.
Accordingly, a description of the dynamic state will be the next:
∀𝑆𝑆�𝑆𝑆 ⊂ (𝑋𝑋1 ,× … × 𝑋𝑋𝑛𝑛 ) × 𝑍𝑍𝑥𝑥 × (𝑌𝑌1 ,× … × 𝑌𝑌𝑛𝑛 )�
∃𝑆𝑆𝑓𝑓 �𝑆𝑆𝑓𝑓 ⊂ (𝑌𝑌1 ,× … … × 𝑌𝑌𝑛𝑛 ) × 𝑍𝑍𝑥𝑥 �, if (7)
𝐹𝐹�𝑆𝑆0 ◻ 𝑆𝑆𝑓𝑓 � = (𝑆𝑆1 + 𝑆𝑆2 + ⋯ + 𝑆𝑆𝑛𝑛 ),
where 𝑆𝑆𝑖𝑖 ⊂ (𝑋𝑋𝑖𝑖 × 𝑌𝑌𝑖𝑖 ) - functionally controlled in the state space and the target space.
Figure 3: Basic structural components of system aggregation.
Figure 4: Structure of the system with feedback.
The concept of autonomy means that after the introduction of feedback, each component of
the output signal {𝑦𝑦𝑖𝑖 } can be changed only after changing the input action {𝑥𝑥𝑖𝑖 }, while the output
𝑦𝑦𝑖𝑖 , 𝑗𝑗 ≠ 𝑖𝑖 the control action does not affect the change in the state of the system with the target
strategy [4].
The functional controllability of the system means that an appropriately selected input
control action (𝑋𝑋/𝑈𝑈/Start 𝑈𝑈(𝐶𝐶𝐶𝐶)), according to the target control strategy, can bring the
system to the target area 𝑉𝑉𝐶𝐶𝐶𝐶 , i.e.
∀ 𝐹𝐹𝑖𝑖 (𝑡𝑡𝑖𝑖 )∃(𝑈𝑈𝑖𝑖 ): ∃ Start (𝑈𝑈𝑖𝑖 /𝐶𝐶𝑖𝑖 ); ∃𝑋𝑋 ≡ 𝑈𝑈𝑖𝑖 ; 𝑈𝑈𝑖𝑖 : 𝑋𝑋 → 𝑌𝑌𝑖𝑖 ∈ 𝑉𝑉𝐶𝐶𝐶𝐶 → [𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆].
Autonomous operation of the energy-active system.
If S is a multidimensional functional system
𝑆𝑆: (𝑋𝑋𝑥𝑥 𝑍𝑍𝑧𝑧 ) → 𝑌𝑌, 𝑋𝑋 = (𝑋𝑋1 × … × 𝑋𝑋𝑛𝑛 ) 𝑎𝑎𝑎𝑎𝑎𝑎
𝑍𝑍𝑥𝑥 = (𝑍𝑍𝑥𝑥1 × … × 𝑍𝑍𝑥𝑥𝑛𝑛 ), 𝑌𝑌 = (𝑌𝑌1 × 𝑌𝑌2 × … × 𝑌𝑌𝑛𝑛 ),
then there is a feedback given in the form of the structure 𝑆𝑆𝑓𝑓 , then it is autonomous and
represented in the form of a parametric (𝑋𝑋 𝑛𝑛 × 𝑇𝑇) description
(∀𝑦𝑦 ∈ 𝑌𝑌)�∃(𝑋𝑋 × 𝑋𝑋𝑥𝑥 )�; (𝑋𝑋 × 𝑍𝑍𝑥𝑥 ) ⇒ (𝑦𝑦 = 𝑆𝑆(𝑥𝑥, 𝑧𝑧)), (8)
where 𝑆𝑆𝑓𝑓 : 𝑌𝑌 → 𝑍𝑍𝑥𝑥 is the substructure that ensures the autonomy of the system.
To implement the operation of mixing the input signal with the feedback signal, the element
H is introduced, which is an operation 𝐴𝐴𝐻𝐻 (+, −, 𝐾𝐾𝑛𝑛 ) of positive and negative feedback and
implements the input stage of the system with feedback (Fig. 5), which represents the dynamics
of changes in the state trajectory (y is a parameter, 𝑦𝑦(𝑡𝑡𝑖𝑖 ) ∈ 𝑌𝑌, 𝑡𝑡𝑖𝑖 ∈ 𝑇𝑇𝑚𝑚 ) of an energy-active object
due to the impact of threats or information disorientation on the control process.
In accordance with the target task, a structural diagram of an automatic tracking system
with information feedback is formed, which transmits signals of changes in the state of the
object under the influence of the input control signal and interference with the functioning of
the control object (Fig. 5):
[𝑋𝑋 ⊗ (𝑍𝑍 − 𝑉𝑉𝑛𝑛 )] → (𝑆𝑆𝑜𝑜 ) → (𝑌𝑌𝑖𝑖 , 𝑍𝑍𝑖𝑖 ) → (State)
𝑉𝑉𝐾𝐾 = [𝐴𝐴(𝑆𝑆𝑡𝑡 ) ⊗ 𝑍𝑍𝑖𝑖 ] → (shifting... trajectory)
Figure 5: Structure of the system with feedback.
To ensure functional stability, the trajectory stabilization condition is met according to the
specified conditions:
(∀𝑥𝑥 ∈ 𝑋𝑋, ∀𝑥𝑥0 ∈ 𝑋𝑋0 , ∃z ∈ 𝑍𝑍x ): [𝑋𝑋0 = 𝐻𝐻(𝑥𝑥, 𝑧𝑧)], and
[H(𝑥𝑥, 𝑧𝑧) = H(𝑥𝑥 ′ , 𝑧𝑧)] ⇒ (𝑥𝑥 = 𝑥𝑥 ′ ),
[H(𝑥𝑥, 𝑧𝑧) = H(𝑥𝑥1 , 𝑧𝑧1′ )] ⇒ (𝑧𝑧 = 𝑧𝑧 ′ ),
∀𝑦𝑦�, ∃(𝑥𝑥�, 𝑧𝑧̂ ): (𝑦𝑦� = (𝐻𝐻 ◻ 𝑆𝑆0 )(𝑥𝑥�, 𝑧𝑧̂ )),
�0 ��.
∀𝑦𝑦�, ∃�𝑋𝑋�0 �: �𝑦𝑦� = 𝑆𝑆0 �𝑋𝑋
3.1.5. Terminal dynamic systems of energy-active class
Terminal dynamic 𝑇𝑇𝑚𝑚 - systems are functional and, due to the internal development of control
actions, are determined on the basis of a representation in the form of a logical structure
[14,15,16]:
∀𝑡𝑡, ∀𝑥𝑥, 𝑋𝑋𝑥𝑥�, �X/𝑇𝑇� 𝑡𝑡 = 𝑋𝑋�/𝑇𝑇� 𝑡𝑡 � ⇒ (S0 (x)/𝑇𝑇� 𝑡𝑡 = S0 (x�)/𝑇𝑇� 𝑡𝑡 ), (9)
that is (S0 /𝑇𝑇� 𝑡𝑡 ), the system is functional ∀t ∈/𝑇𝑇� 𝑡𝑡 .
For such systems, the unambiguity of functionality is determined in accordance with the
condition of management sustainability and adequacy of the structure to the goals:
If ∃𝑆𝑆, 𝑆𝑆 ⊂ (𝑥𝑥 × 𝑍𝑍𝑥𝑥 ) × 𝑌𝑌) - the system, then according to goals ∃strat 𝑈𝑈�𝐶𝐶 ∃𝑆𝑆𝑓𝑓 , 𝑆𝑆𝑓𝑓 ⊂
𝑖𝑖
(𝑌𝑌 × 𝑍𝑍𝑥𝑥 )𝜗𝜗𝜗𝜗�𝑆𝑆𝑆𝑆𝑆𝑆𝑓𝑓 � = 𝐹𝐹𝑠𝑠 �𝑆𝑆𝑓𝑓 � determines that is functional and unbiased, then the trajectory
equation has the form:
∀𝑧𝑧 ∈ 𝑇𝑇, (∃(𝑥𝑥, 𝑦𝑦, 𝑧𝑧) ∈ 𝑆𝑆)𝜗𝜗((𝑥𝑥�, 𝑦𝑦�, 𝑧𝑧̂ ) ∈ 𝑆𝑆)𝜗𝜗((𝑧𝑧, 𝑦𝑦)|𝑇𝑇� 𝑧𝑧 = (𝑧𝑧̂ , 𝑦𝑦�)|𝑇𝑇� 𝑡𝑡 ) ⇒ (𝑥𝑥|𝑇𝑇� 𝑡𝑡 = 𝑥𝑥�|𝑇𝑇� 𝑡𝑡 ) (10)
and the system 𝐹𝐹𝑠𝑠 �𝑆𝑆𝑓𝑓 � ∣ 𝑇𝑇� 𝑡𝑡 is unambiguously functional.
For hierarchical systems, the condition of unambiguous functioning of all systems ensures
the functional stability of the structure; if such conditions are violated, the system will
experience limit and emergency modes, structural collapse, loss of controllability, and disasters.
For the functional controllability of the required system, it is enough to make the system
( S = H S0 ) autonomous with the help of a communication loop Sf.
Based on the above analysis of the structure and functionality of hierarchical systems and
the impact of external and internal threats on control modes, there is a draw of conclusion about
the training of operational personnel and their knowledge.
The modern development of the science of intelligence is based [4] on three aspects of
cognitive functioning that were not taken into account in the IQ-concept, respectively:
competence (conscious knowledge base); pragmatism of thinking procedures; mental potential
for problem solving.
The blocks of knowledge necessary for performing professionally oriented activities are
formed in the process of learning and work based on the ordering of the knowledge acquired
in the past and the amount of new knowledge.
Gradation of stages of knowledge accumulation:
1. quality of school education as a basis for professional orientation;
2. technical education (vocational schools, colleges, workshops);
3. engineering and university education in the area of specialization of each student;
4. professional activity in the chosen field and assessment of compatibility with the
requirements for efficiency and responsibility;
5. professional work of the highest rank, understanding of the independence of training,
internships, doctoral studies for strategic level positions.
In accordance with the stages of knowledge accumulation, let’s build a table of information
and cognitive suitability of operational personnel (Table 2).
Table 2
Information and cognitive fitness of operational personnel
# Cognitive fitness index KF α risk
1 Ability to perform active management actions (ZAd) 0.55-1.5 α r < 0.2
2 Focused on recognizing the situation (CSitПS) 0.85-1.5 α r < 0.25
3 Impact of active attack factors and threats (Rek (AF)) 0.65-1.5 α r < 0.5
4 Correlation to goal-oriented activities under the 0.75-1.5 α r < 0.3
influence of threats (CDi))
5 Multiple targeted alternatives for action selection (C(Di)) 0.95-1.5 α r < 0.25
6 Developing a strategy to eliminate threats (VStrarU) 0.85-1.5 α r > 0.5
7 Cognitive selection of sequential actions to target and 0.75-1.5 α r > 0. 5
eliminate attacks (КSv(Ci))
8 Targeted selection of a course of action during an attack 0.85-1.5 α r < 0.2
ПSv(Ci)
9 Conscious risk assessment in case of life threat α risk 0.75-1.5 α r < 0.25
10 Formation of consistent actions in the system under the 0.65-1.5 α r > 0.5
influence of threats (FIcon Sit)
11 Choosing a way to counteract information attacks and 0.75-1.5 α r > 0.5
understanding the nature of the situation (Sens (Icon))
12 Understanding the essence of the image of the target 0.75-1.5 α r > 0.5
situation in attacks (Sens (Ci))
13 Active counteraction in case of threats to the targeted 0.55-1.5 α r > 0.5
operations (Di(Ci/Ui))
14 Operator confidence in their actions ( KV sp ) 0.85-1.5 α r > 0.2
15 Comprehensive operator confidence and intelligence ( 0.7-1.5 α r > 0.2
S g K V ( Аі ) ZpKV (А j ) ) 0.65-1.5 α r > 0.3
16 Operator confidence in their knowledge ( SKV ( Аі ) ) 0,85-1,5 α r > 0.5
17 Professional self-confidence of the operator ( S Z КV ( Аі ) ) 0,85-1,5 α r > 0.7
18 Trust of external experts in the identity of the operator ( 0,25-1,5 α r > 0.5
Rd ( Аі ) )
19 Professional credibility of a cognitive agent ( K ZP ( Аі ) ) 0,25-1,5 α r > 0.5
20 Self-confidence in the ability to solve the problem ( 0,75-1,5 α r > 0.8
К cogn ( Аі ) К du (А ) ) 0,85-1,5
21 Determination to act in the face of risk ( К d (Drisk ) 0,85-1,5 α r > 0.75
К d (D(Сі )) 0,95-1,5
where (α risk ) - risk assessment, ( K d ) - cognitive trust coefficient, ( К V ) - coefficients of
knowledge requirements.
4. Conclusion
The article considers certain aspects of the use of logical and intellectual procedures that form
the basis of the scheme for synthesizing hierarchical control systems.
Based on the construction of hierarchical systems with different functional structure, an
approach using the logic of actions and the theory of situational management is proposed,
models of the structure of systems for active control of technological processes under conditions
of dynamic disturbances, both systemic, structural and cognitive-informational types, are
developed.
The concept of goal orientation and coordination of the logical and cognitive model of
forming control decisions of a system with a hierarchical structure under conditions of threats
and information attacks as a basis for the synthesis of robust decision-making strategies in crisis
emergency situations is substantiated.
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