=Paper=
{{Paper
|id=Vol-3887/paper12
|storemode=property
|title=Methods and Models for Building Adaptive Automated Systems of Organizational Management
|pdfUrl=https://ceur-ws.org/Vol-3887/paper12.pdf
|volume=Vol-3887
|authors=Aleksandr Dodonov,Aleksey Nikiforov,Vladimir Putyatin
|dblpUrl=https://dblp.org/rec/conf/its2/DodonovNP23
}}
==Methods and Models for Building Adaptive Automated Systems of Organizational Management==
https://ceur-ws.org/Vol-3887/paper12.pdf
Aleksandr Dodonov1, Aleksey Nikiforov1 and Vladimir Putyatin1
1
Institute of Information Registration Problems of the National Academy of Sciences of Ukraine, Shpaka street, bldg. 2, Kyiv,
03113, Ukraine
Abstract
The adaptation of automated organizational management systems (ASOM) is closely related to the concept
of distributed systems. In this context, adaptation involves modifying structural relationships between
information blocks, adjusting processing algorithm parameters, and incorporating reflective elements.
Currently, the field of ASOM adaptation within complex distributed systems has emerged, where specialized
mathematical models and methods are employed. This paper presents an analysis of the scientific and
methodological framework for ASOM adaptation, including examples of successful applications of ontology
synthesis and conceptual structure synthesis using degree-based structural typologies. Limitations of current
approaches in addressing adaptation challenges, particularly with respect to conceptual changes, are
identified. Further development directions are suggested, focusing on enhancing the scientific and
methodological framework through tensor transformations in electrical multicoil networks.
Keywords
Automated Management System, Organizational Management, Adaptation, Conceptual Design, System
Algebra, Set Degrees, Theoretical-Systemic Construct, Conceptual Scheme, Constituent, Confinement
Model, Ontological Universality, Types of Structures.1
1. The problem of ASOM adaptation
Automated Systems of Organizational Management (ASOM) consist of the following elements
(Figure 1):
System Model: Includes a description of functioning and management processes
(decision-making) and a logical model of the corresponding database aligned with this
description.
System of Output Data: Incorporates decision-making rules or axioms.
System of Computational Procedures: Encompasses information processing and
transformation procedures.
Typically, ASOM are tailored to specific conditions, with processes structured in defined control
loops that provide partial adjustability within a specified range of external conditions. However, with
the emergence of new, previously unconsidered tools, methods, interconnections, and relationships
between management elements, ASOM can quickly become outdated. Consequently, the need arises
to adapt ASOM to new management concepts. Attempts to revise and modernize ASOM often lead to
software conflicts and contradictory situations, making it easier at times to initiate a new project
rather than upgrade an existing system.
ITS-2023: Information Technologies and Security, November 30, 2023, Kyiv, Ukraine
dodonovua@gmail.com (A. Dodonov); aleksey.nikiforov.62@gmail.com (A. Nikiforov);
putvlgr@gmail.com (V. Putyatin)
0000-0001-7569-9360 (A. Dodonov); 0000-0002-0207-5175 (A. Nikiforov); 0000-0002-5575-9159 (V. Putyatin)
© 2023 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
134
Workshop ISSN 1613-0073
Proceedings
The emergence of new means and methods of their
application
Designed automated organizational management system
System model
Description of Logical
functioning database Source data system (axioms
and model of management)
management
processes
System of information
processing procedures
The problem is that: introducing new settings or changing software
leads to conflict situations. It is easier to develop a new automated
control system than to adapt its current version.
Figure 1: Key Structural Elements of ASOM and the Problem of Their Adaptation.
As technological cycles shorten, the urgency of adapting ASOM structures or concepts intensifies.
Such adaptation ideally should occur without a complete redesign or the need for new automation
tools, instead relying on transformative procedures that require minimal time and resources.
Therefore, when designing new ASOM, it is advisable to integrate adaptability features, preferably in
an automated manner.
To address ASOM adaptation, several key research directions should be emphasized. The
organization management process operates in three modes (Figure 2):
Planning or Programming Mode: Focused on preparing for future operations.
Adjustment Mode: Modifies a pre-existing plan during its execution (targeted
management).
Operational Management Mode: Manages ongoing operations in real-time.
The problem of adaptation of AOMS to
conceptual changes in management
processes
Planning or Programming Adjustment Mode (target Operational Management
Mode: management): Mode:
1) adaptation of the control 1) transformation of the area 1) adaptation of algorithms
object model (structure and of controlled parameters; for restoring the current state of
behavior); 2) changing the boundaries the system in relation to current
2) adaptation of algorithms and dimensions of the zones of management criteria;
for predicting the state of the permissible and boundary- 2) adaptation of algorithms
system under given control and achievable parameters. for diagnosing functional
conditions; deviations, risks, threats, etc.
3) adaptation of algorithms
for selecting optimal control for a
given terminal state of the
system.
Figure 2: Management Modes and Current Research Directions for Addressing ASOM Adaptation
Issues.
135
Achieving ASOM adaptation to a new management concept during the planning mode requires
mechanisms that transform:
1. Management Object Model: Restructures the management process to align with a new
conceptual framework, including functional relationships and responses to external influences.
2. Prediction Algorithms: Adjusts ASOM software to predict the system's state under the new
management model and external conditions.
3. Optimal Management Algorithms: Updates decision-support algorithms to plan for the
organization’s functioning under the modified model and performance criteria.
For the adjustment mode of previously created plans, transformation mechanisms include:
1. Controlled Parameter Areas: Expands the parameters, dimensionality, and structure of
inter-parameter relationships.
2. Acceptable and Limit-Reachable States: Adapts criteria for achieving established goals.
For operational management, transformation mechanisms involve:
1. Current State Algorithms: Reflects observed parameters in the cognitive model of the
management process.
2. Diagnostic Algorithms: Identifies functional deviations, risks, etc.
3. Decision Support Algorithms: Provides real-time support for current management
decisions.
This detailed breakdown of the adaptation problem highlights the importance of developing
mathematical and software solutions for ASOM. Targeted research in these areas will lay the
theoretical groundwork for adaptive ASOM development. Some scientific advancements have already
been made in synthesizing structures with defined properties and in the conceptual design of complex
systems.
2. Mathematical Models and Methods for Constructing Adaptive
ASOM
In constructing adaptive Automated Systems of Organizational Management (ASOM), two primary
approaches, closely linked through ontology application, can be identified (Figure 3):
System Algebra Framework: Utilizes Boolean functions, predicate calculus, and logical
inference [1].
Set Degree or Structure Type Framework: Also known as conceptual design [3], this
approach relies on degrees or types of structures [2].
The system algebra framework combines mathematical logic with algebraic structures, such as
groups and rings, which serve as models for processes, and lattices, which model structural
relationships. The set degree framework similarly employs algebra but focuses on set degree
formation and logical procedures. Together, these approaches support the development of adaptive
mechanisms for systems, with multiple successful implementations already demonstrated.
2.1. Confinement Models
As proposed in [4], confinement models (CM) provide a structured approach to building
ontologies, allowing a systemic-cognitive method that remains impartial to individual researchers'
modeling techniques. Using CMs, original ontologies are constructed based on ontological universals,
which model relational systems across various subject areas.
136
System algebra apparatus
|
|
|
Mathematical logic | Algebra, algebraic Apparatus of stages of sets
(Boolean functions, | structures (groups, (kinds of structures).
predicate evaluation, | rings, lattices). Conceptual design.
logical inference). |
|
|
|
Ontological approach
Figure 3: Mathematical Models and Methods Used to Solve the Problem of ASOM Adaptation.
The following types of confinement models are identified (Figure 4):
Conceptual CM (CCM): Connects elements through "causes/depends on" relationships,
with a specific case being the triadic CM (TCM) (Figure 4a).
6
8 2
6
7 3
8 5
7 2 1
9 4
9 1 3 5
4 Is
a b
6
8 2
8 6 5
7 3
7 2
9
1 4 9 1 3
5 4
Is a part Has the
property
c d
Figure 4: Types of Confinement Models: a) CCM; b) GCM; c) MKM; d) AKM
137
Hierarchical CM (HCM): Includes various forms:
o Hypernymic (HCM) (Figure 4b): Classifies concepts using hierarchical genus-
species relations, expressed as "is."
o Meronymic (MKM) (Figure 4c): Analyzes subsystems systematically with "is part
of" relationships.
o Attributive (AKM) (Figure 4d): Classifies properties using the relation "has a
property."
Process CM (PKM): Structures processes by identifying life cycle stages with "is
input/output for" relationships.
Through CMs, knowledge structuring can be achieved using interrelated cognitive models of a
specialized kind, setting a standard for ontology detailing by various researchers. This approach
facilitates the development of formal methods for operating and transforming ontology structures.
2.2. Automatic Adaptation of Information Processing Algorithms
In [5], ontological task models are proposed for developing software systems capable of adapting
to changes in a given domain. Here, a “task” in the task ontology refers to a structured problem
situation defined by specific conditions and goals (criteria). The domain ontology represents the
management process as a series of elementary tasks. A formal ontological model is constructed using
system algebra [1], and practical algorithms for transforming task ontologies are implemented in the
CLEPE environment (Conceptual Level Programming Environment), adhering to principles of
conceptual modeling [3].
In the modeling system, knowledge is formally represented as follows:
The domain consists of a set of objects
𝐴 ,𝐴 ,… ,𝐴 ,
where each object is classified as an instance of a corresponding concept. These object sets serve as
the basis for n many-sorted algebras.
Each set 𝐴 , defines an abstract data type:
𝐸 = (𝑁𝑎𝑚𝑒, Σ, 𝐸 ), (1)
where 𝑁𝑎𝑚𝑒 denotes the type name (e.g., circle); Σ is the signature of the many-sorted algebra (circle
parameters like center coordinates, radius); 𝐸 is the defining relations of the type (circle equations).
An algebraic domain set is formed by types 𝐸
𝐸 = (𝐸 , … , 𝐸 , … , 𝐸 ). (2)
Additional domains are defined as follows:
Attribute Domain, 𝐴𝑡, defined as key-value pairs:
{𝑘𝑒𝑦, 𝑣𝑎𝑙𝑢𝑒} ,
where 𝑘𝑒𝑦 is the attribute identifier (for example, "x"); 𝑣𝑎𝑙𝑢𝑒 - its value (real number). Operations
such as merge, substitute, delete, and interpret (merge, substitute, delete, enterp) are defined for
this domain. In addition to these operations, various functions are defined, for example, the value
selection function of the domain:
𝐹 (𝐴𝑡, 𝑘𝑒𝑦) → 𝑣𝑎𝑙𝑢𝑒 ;
Boolean Domain, 𝐶𝑠, contains expressions yielding Boolean values {𝑡𝑟𝑢𝑒, 𝑓𝑎𝑙𝑠𝑒} with
variables from other domains. It includes Boolean operations "AND," "OR," "otherwise" and
simplifies conditions via the interpretation operation (=). 𝐶𝑠 elements are constraints (conditions).
Entity Domain with Attributes, 𝑇, represented by tuples
𝐸 , 𝐴𝑡 , 𝐶𝑠 ∗ ,
138
where for each i there is only one j, that forms an element of the T:
∀𝑖 ∃ 𝑗: 𝐸 , 𝐴𝑡 ,
each condition (constraint) belonging to the subset 𝐶𝑠 ∗, is an expression with operands belonging
to the domain 𝐴𝑡 . Operations on elements of this domain are the union or division (merge, split)
of entities. The union operation is interpreted as the synthesis of a new entity with a compatible
set of properties and constraints (conditions) of operand entities. The division operation is the
reverse. Instances of the domain of entities with attributes are tuples of corresponding facts;
Relation Domain, RI, on structures:
𝑇 , × … × 𝑇 , , 𝐴𝑡 , 𝐶𝑠 ∗ ,
where 𝑇 , × … × 𝑇 , is a Cartesian product of algebraic data types from the 𝑇 domain (attribute
space related to the i-th structure); 𝐴𝑡 - types of relation attributes; 𝐶𝑠 ∗ - constraints (conditions)
defining the relation. Operations such as union, separation, substitution (merge, split, substitute)
are performed on relations.
The ontology itself is a tuple of concept domains with attributes, relations, and constraints:
𝑂𝑛 = (𝑇, 𝑅𝐼, 𝐶𝑠 ∗ ). (3)
The problem’s ontological model is described by the tuple:
𝑀𝑑 = 〈𝑂𝑛 , 𝐴𝑐 ∗ , 𝐶𝑠 ∗ 〉 , (4)
∗
where 𝑂𝑛 is the problem ontology according to the construction rules (3); 𝐴𝑐 is the task
ontology; 𝐶𝑠 ∗ is the set of additional constraints (conditions). Each action is an entity within the 𝑇
domain, serving as a command to external services or other ontological models. Parameters are
attributes from 𝑂𝑛 or constants.
The transformation of algorithms depending on changes in conditions and constraints is carried
out using the parameter initialization function (InstPar), which is given as a set of mappings between
the action attribute and the attribute values of entities and relations in the ontology model:
𝐼𝑛𝑠𝑡𝑃𝑎𝑟: 𝐴𝑐 , , 𝑝𝑘𝑒𝑦 , → 𝑆𝑒𝑙𝑉𝑎𝑙 𝐴𝑡 , , 𝑘𝑒𝑦 , , (5)
𝐴𝑐 , ∈ 𝑀𝑑 , 𝐴𝑡 , ∈ 𝑂𝑛 ∈ 𝑀𝑑 ,
where 𝑀𝑑 is the ontological model of the considered task; 𝑂𝑛 is the task’s ontology.
The software system based on the ontological model of tasks is presented in Figure 5 [5].
Simulation system Knowledge base
Web sites
Ontology
Semantic interpretation of facts.
Document
repositories Services and
modeling systems
Extensions to
the description Description
Log files Fact base of ontology of models
Model execution classes and using
manager relations. ontology.
Establishing the
fact of the process.
Database Information
service provider Interpreting facts, solving
tasks, establishing
Web Model interaction relationships. Models
services broker
Requests to the provider during
model execution.
Using operations
Semantic interpretation of events. by calling external
services.
External
Events
services
Figure 5: The structure of a software system based on ontological task models.
139
The management process in the intelligent control system generates events, which are interpreted
using the ontology of the corresponding subject area. Based on the interpretation of the event, models
and algorithms necessary for implementing the computational process for management in current
conditions are activated. Using the ontology of models and algorithms, a new computation schedule
is created. The synthesis of the schedule is carried out using the apparatus of mathematical logic
(logical inference).
Depending on the context of the occurring events, either one or another ontological model is
activated. The initiator of activation is the ontological model being executed (Figure 6) [5].
Activator model Activated model
Defining Initializing the Identifying
Model
the Goal General Model Relevant Initialization
selection
Models
Execution in a specific context.
Context
Figure 6: The process of activating a task model.
This framework also supports the creation of new ontologies. This involves the following steps:
1. Analyzing the problem and identifying relevant entities, relations, constraints, and
operations.
2. Constructing the ontological model using available components, supplemented with any
newly identified elements.
3. Validating the updated ontology and resolving contradictions.
The ontology-based tool for building software systems offers functionalities including:
Ontology Operations: Creation and modification of ontology classes, relationships, and
attribute constraints.
Fact Operations: Creation and modification of individual facts, constraint verification, and
fact validation.
Ontological Model Management: Creation and editing of models using classes and facts,
defining constraints, operations, and service links.
Execution of Models: Testing models on a factual base and verifying outcomes.
The system is implemented in Python with PyQt for its graphical interface, and includes
components such as an ontology editor, fact editor, model editor, and simulation programs. Future
development will focus on expanding model interactions, implementing logical inference, enabling
multi-variant computations, and addressing contextual dependencies.
2.3. Deployment of Security Domain Ontology Based on Conceptual Schemes
of Abstract Security Relations
In [6], a methodology is outlined for modeling the "security" domain using conceptual analysis
and design, specifically focusing on a mixed inter-subjective and subject-object security relation
derived from an abstract security structure. This approach is based on several key postulates for
security relations [7]:
There exists a world of possibilities.
A possibility can be actualized and then ceases to be a possibility.
140
An element of the world of possibilities is the possibility of realizing one or another event.
Possibilities can be connected by a "genetic" relation (the realization of one or several
possibilities is a necessary condition for the realization of another possibility).
Possibilities can be linked by a blocking relation (if a blocking possibility is realized, a blocked
possibility cannot be realized).
Possibilities are attributes of subjects and objects in the "real world" that realize these
possibilities.
There exists a world of subjects.
Subjects have interests.
The interests of different subjects can enter into relations.
Relations between subjects occur only through their interests.
In the world of possibilities, complex network structures with cycles can emerge.
A subject's interests nominally constitute a subset of its possibilities (the subject is interested in
realizing these possibilities).
Any possibility that blocks possibilities from the subject's area of interest represents a threat to
the subject's interests.
A possibility that blocks a threat is a security measure concerning that threat.
An action to realize a possibility is a possibility that is formative for the subject related to that
possibility.
Since threats and actions regarding the realization of possibilities can also define threats and
measures, it can be said that there are first, second, third, etc., order threats and measures.
The ontology construction process involves iteratively breaking down the factors in a structure-
tree format within this set of possibilities. This breakdown involves:
Concept Elaboration: Specification and detailing of initial concepts.
Inter-branch Relations: Formation of relations between ontology branches by integrating
hierarchical levels and factor-based relationships.
Using conceptual schemes of abstract security relation structures [7], the ontology's factor-
structure is built, including types like:
Abstract Security Relations: Basic interconnections and constraints among possibilities.
Hierarchical Subject-transforming Security Relations: Transformational security
relationships at different subject levels.
Polysubjective Security Management: Relations involving multiple subjects managing
shared security interests.
Danger Propagation: Mechanisms for identifying and propagating security threats across
the structure.
A fragment of Security Structure Types is provided in Table 1.
Table 1
The conceptual scheme of types of structures of abstract security relations (fragment)
Denotation of Formal expression of constituents Schematic interpretation of
constituents constituents
𝑋1 Set of possibilities.
𝑋2 Set of subjects.
𝐷1.1 ℬ(𝑋1 × 𝑋1) Relationship of genetic connection of
possibilities or set of pairs: possibility -
possibility, which proves to be a
necessary condition for the realization
of the considered possibility.
141
𝐷1.2 ℬ(𝑋1 × 𝑋1) Relationship of blocking connection of
possibilities or set of pairs: possibility -
possibility that blocks the considered
possibility.
𝑇1.0 {𝛼 ⊂ ℬ(𝑋1 × 𝑋1)|Pr 𝛼 = Pr 𝛼} Set of cycles of possibilities.
𝐴1.1 (𝛼 ⊂ 𝑇1.0)&(𝛼 ⊂ 𝛽) ⇒ (𝛼 ⊂ Axiom. Relations of genetic, blocking,
𝐷1.1) ∨ (𝛼 ⊂ 𝐷1.2) ⇒: (𝛽 = ∅) as well as mixed genetic and blocking
connection of possibilities do not allow
cycles and loops.
𝐴1.2 𝛼 ∈ ℬ(𝑋1 × 𝑋1) & Axiom. Possibilities connected by a
(𝑑 ∈ 𝛼) ⊃ (𝑑 ⊂ 𝐷1.1) & genetic relationship cannot be
(𝑥 ∈ Pr 𝛼)&(𝑥 ∈ Pr 𝛼)& connected by a blocking relationship,
(Pr 𝛼\𝑥 = Pr 𝛼\𝑥 ) ⇒ and vice versa.
𝛽 ∈ ℬ(𝑋1 × 𝑋1)&(𝑑 ∈ 𝛽) ⇒
¬
(𝑑 ⊂ 𝐷1.2)&(𝑥 ∈ Pr 𝛽)&
(𝑥 ∈ Pr 𝛽)&(Pr 𝛽\𝑥 = Pr 𝛽\𝑥 )
⋮ ⋮ ⋮
Constituents presented in Table 1 are types of abstract security relation structures synthesized
using formal rules of transforming text structure when applying set degree formation operations [7].
The handbook of theoretical constructs [8] based on this procedure contains over 200 system
classes, covering both static systems (fixed relations) and dynamic (degrading) systems, facilitating a
deductive approach to security management system design—from abstract principles to concrete
applications. A key challenge remains in interpreting high-degree set constituents, which, due to their
complexity, require specialized tools for practical use.
3. Development of Adaptation Methods and Models for ASOM
3.1. Current Challenges in Adaptation
The scientific results presented are an example of a fairly successful solution to the problem of
adapting ASOM. However, it cannot be claimed that the problem is fully solved. There are limitations
and drawbacks to the methods that do not allow concluding the completion of creating a conceptual
transformation apparatus for management systems.
Therefore, when adapting the computational procedures' regulations (see section Помилка!
Джерело посилання не знайдено.), the ontology of models and algorithms is used, which is pre-
formed and entered into the knowledge base. The task of expanding and developing the ontology
based on the interpretation of facts and events remains unresolved. This leads to the need, once again,
to create a new version of the mathematical and software when there are conceptual changes in the
management process for which the ASOM is created. The adaptation or "learning" of ASOM under a
new management concept has not yet been implemented.
For the method of using conceptual schemes of structure types (see section Помилка! Джерело
посилання не знайдено.), the bottleneck is the interpretation of the created abstract schemes. For
higher set degrees (which are significant in practice), the generated constituents are expressions with
a very large dimension. Their size exceeds human capabilities to operate with data blocks. In [8], to
overcome this difficulty, it is suggested to create a special language for the formalized description and
representation of set degrees. In both cases, the essence of the difficulties hindering the
142
implementation of ASOM adaptation lies in creating a method and corresponding software for
synthesizing structures with specified properties.
3.2. Proposed Solutions to Adaptation Challenges
As a method for synthesizing new structures, tensor transformation of networks developed by
Gabriel Kron [9] can be used. Kron proposed a methodology for the theoretical-set and algebraic
synthesis of topologies in the form of the analysis method and tensor transformation of electrical
networks.
An electrical network is convenient for a formalized description of structural connections of
various kinds. Unlike other types of non-electric networks, an electrical network is always
surrounded by a dynamic electromagnetic field created by itself, extending to infinity in all directions.
By using the model of induction and self-induction in the branches of an electrical network, it is
convenient to describe various intra-system connections between elements of the analyzed structure
(organizational topology).
If we interpret the organizational-functional structure in the form of a multi-coil electrical
network, tensor synthesis of Kron [9] can be used to synthesize a structure with specified properties.
The synthesis tensor is defined as follows:
For an existing multi-coil electrical network, there is a connection tensor 𝐂 or in other words, a
primitive network transformation tensor. A primitive network is a set of node pairs (an electric coil
with an input and output point) and elementary circuits that form a specific network but are not
connected to each other. The transformation tensor 𝐂 is such that the corresponding electrical
network functions in a defined manner:
𝑄(𝐳 , 𝐢 , 𝐞 ) = 0 , (6)
where 𝐳 is the impedance tensor (electrical resistances of node pairs and network circuits, taking
into account the resistance of inductance and self-induction in mutual influence of coils),
𝐢 is the current tensor;
𝐞 is the voltage tensor;
𝑄(𝐳, 𝐢, 𝐞) = 0 is the formalized representation of the network's behavior.
The impedance tensor of the output network 𝐳 is derived from the impedance tensor of the
primitive network 𝐳′ using the transformation tensor (𝐂 ) [9]:
𝐳 = (𝐂 ) 𝐳′ 𝐂 . (7)
The synthesis tensor 𝐂 is derived to transform the impedance tensor of the output network 𝐳
into the impedance tensor of another network 𝐳 , without changing the network's behavior:
𝐳 = (𝐂 ) 𝐳 𝐂 , (8)
𝑄(𝐳 , 𝐢 , 𝐞 ) = 𝑄(𝐳 , 𝐢 , 𝐞 ) = 0 , (9)
where (𝐂 ) is the transposed synthesis tensor 𝐂 .
The method of deriving the synthesis tensor 𝐂 depends on the form of the formalized description
of the system behavior 𝑄(𝐳, 𝐢, 𝐞). The result of this derivation is a compound tensor (a tensor whose
elements are also tensors) [9].
In [10], a method for the formalized representation of conditions for computing regulations based
on the transformation of a multi-coil network is provided. The condition is expressed as the equality
of zero currents in intermediate node pairs of the network. Intermediate node pairs are interpreted as
a group of parameters not determined in the process of computations. Using the synthesis tensor, a
variety of electrical networks satisfying the formalized description of the system behavior 𝑄(𝐳, 𝐢, 𝐞)
{𝐳 , 𝐢 , 𝐞 } ∈ Ω ,
where Ω – is the set of electrical networks obtained by transforming from the output network
{𝐳 , 𝐢 , 𝐞 } using the synthesis tensor 𝐂 , determined based on the formalized condition (6).
143
The choice of a specific network {𝐳, 𝐢, 𝐞}∗ from the variety Ω is made using an established
criterion 𝐾:
𝐾{𝐳,𝐢,𝐞}∗ ≻ ⋯ ≻ 𝐾{𝐳 ,𝐢 ,𝐞 } ≻ ⋯ ≻ 𝐾{𝐳 ,𝐢 ,𝐞 } , (10)
where 𝑛 is the number of alternative electrical networks forming the set Ω .
Thus, solving the problem of synthesizing structures with specified properties and addressing the
adaptation problem of ASOM to conceptual changes in the control process can be implemented by
introducing the following intermediate scheme (Figure 7).
Determination of the synthesis
tensor from the conditions
defining the domain of
existence of the transformed
network.
Procedure for
transforming a A new conceptual
Conceptual Conceptual conceptual diagram that meets
diagram 1 diagram 2 ... diagram using the selection
the Kron network criterion
Bank of interpreted synthesis tensor
conceptual diagrams
for specific systems
Criteria for selecting a
conceptual diagram.
Figure 7: Scheme for Obtaining New Structures through Tensor Transformation of Pre-Interpreted
Conceptual Schemes.
This scheme involves using a pre-interpreted bank of conceptual schemes for specific systems.
Conceptual schemes are presented as multi-coil electrical networks with a corresponding formalized
description of the desired behavior. In other words, defining the boundaries of the region of
permissible state parameters or the existence area of the system.
In case of changes in the control loop that cannot be adapted by adjusting parameters within the
existing control structure:
the conceptual schema that is relevant to the initial state of the ASOM is retrieved from the
database. Each conceptual schema has a formalized representation of its domain of existence and
a pre-formed synthesis tensor to determine alternative schemes within that domain;
using the synthesis tensor, a transformation of the original conceptual schema results in a set
of alternative conceptual schemes;
a criterion for establishing preference is formulated for comparing these alternative
conceptual schemes;
the criterion previously established is used to determine and choose a new conceptual scheme
that best meets the needs of adapting the ASOM to the changes that have occurred in the
management process.
Therefore, to address the adaptation problem in this context, progress should be made in the
following directions: creating a database of pre-interpreted conceptual schemes for specific systems
in relevant subject areas; developing a procedure for transforming conceptual schemes based on the
use of the tensor transformation procedure for electrical networks.
Acknowledgements
Methods and models designed to solve adaptation and self-organization problems of Automated
Control Systems (ACS) belong to the field of conceptual ontology design and transformation.
There are examples of developing adaptation models based on the application of:
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confinement models for ontological networks;
algebraic systems apparatus;
set theory apparatus of N. Bourbaki.
The main practical challenge in implementing these approaches is the issue of dimensionality. To
construct adaptive control systems with complexity corresponding to real processes, the problem of
creating a specialized language for interpreting (representing) the results of conceptual design needs
to be addressed.
As an intermediate step in solving the adaptation problem, it is advisable to address the design
task by transforming previously created conceptual schemes of specific systems.
The primary tasks for implementing this approach include:
creating and accumulating a database (bank) of pre-interpreted conceptual schemes for
specific systems;
developing a procedure for transforming conceptual schemes based on the use of the tensor
transformation procedure for electrical networks.
References
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118 p.
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[8] Ivanov A.Yu., Nikanorov S.P., Garayeva Yu.R. Handbook of system-theoretic constructs.
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[10] Oleksandr G. Dodonov, Oleksii V. Nikiforov, Volodymyr G. Putiatin, "Implementation of
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Mathematical Machines and Systems, No. 1, Kyiv, IPMMS NASU (2022). ISSN 1028-9763 – P.
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