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Axioms
Special Issues
Modern Trends and Application of Decision-Making Theory, Stability and Control
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Modern Trends and Application of Decision-Making Theory, Stability and Control

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: 31 August 2025 | Viewed by 1924

Special Issue Editors

Prof. Dr. Valentyn Sobchuk

E-Mail Website
Guest Editor
Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, 4E Academician Glushkov Avenue, 03127 Kyiv, Ukraine
Interests: differential equations; information systems; dynamical systems; nonlinear dynamical systems; functional stability
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Oleksiy V. Kapustyan

E-Mail Website
Guest Editor
Department of Integral and Differential Equations, Taras Shevchenko National University of Kyiv, 4E Glushkov Avenue, 03022 Kyiv, Ukraine
Interests: stability theory; control theory; approximation theory; information technologies

Special Issue Information

Dear Colleagues,

This Special Issue will bring together the state-of-the-art results obtained in sustainability theory, decision making theory, mathematical control problems and their multidisciplinary applications, including with the use of artificial intelligence.

Interest in these topics is constantly growing as a result of the increasing complexity of modern mathematical models, which require the use of information technologies, computer and mathematical modeling, and at the same time, the development of existing and new theoretical approaches in these branches of mathematics. In this Special Issue, we will consider Lyapunov stability and robust stability in evolution equations describing real-world phenomena, the existence and properties of limit modes and attractor sets in impulsive dynamical systems with mechanical applications, the theoretical and practical aspects of approximation theory, decision theory and numerical analysis, optimal and adaptive control in nonlinear systems, and artificial intelligence.

Our goal is to collect articles reflecting new trends and approaches in sustainability theory, decision theory, control theory, applied artificial intelligence and related topics.

Prof. Dr. Valentyn Sobchuk
Prof. Dr. Oleksiy V. Kapustyan
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • nonlinear systems
  • stability
  • perturbation
  • impulsive systems
  • approximation
  • numerical methods
  • control
  • decision making theory
  • machine learning

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (4 papers)

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19 pages, 12884 KiB  
Article
Evolutionary Search for Polynomial Lyapunov Functions: A Genetic Programming Method for Exponential Stability Certification
by Roman Pykhnivskyi, Anton Ryzhov, Andrii Sobchuk and Yurii Kravchenko
Axioms 2025, 14(5), 343; https://doi.org/10.3390/axioms14050343 - 30 Apr 2025
Viewed by 279
Abstract
This paper presents a method for constructing polynomial Lyapunov functions to analyze the stability of nonlinear dynamical systems. The approach is based on genetic programming, a variant of genetic algorithms where the search space consists of hierarchical tree structures. In our formulation, these [...] Read more.
This paper presents a method for constructing polynomial Lyapunov functions to analyze the stability of nonlinear dynamical systems. The approach is based on genetic programming, a variant of genetic algorithms where the search space consists of hierarchical tree structures. In our formulation, these polynomial functions are represented as binary trees. The Lyapunov conditions for exponential stability are interpreted as a minimax optimization problem, using a carefully designed fitness metric to ensure positivity and dissipation within a chosen domain. The genetic algorithm then evolves candidate polynomial trees, minimizing constraint violations and continuously refining stability guarantees. Numerical examples illustrate that this methodology can effectively identify and optimize Lyapunov functions for a wide range of systems, indicating a promising direction for automated stability proofs in engineering applications. Full article
(This article belongs to the Special Issue Modern Trends and Application of Decision-Making Theory, Stability and Control)
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15 pages, 2009 KiB  
Article
Numerical Model for Simulation of the Laser Thermal Forming Process
by Yaroslav Zhuk, Mykola Melnichenko, Arash Soleiman Fallah and Vitalii Husak
Axioms 2025, 14(4), 255; https://doi.org/10.3390/axioms14040255 - 28 Mar 2025
Viewed by 232
Abstract
A numerical model to simulate the laser thermoforming process (LTF) is proposed. It is developed on the basis of the thermodynamically consistent theory of coupled thermo-viscoplasticity and is suitable for modeling the LTF for thin-walled metal structural elements. In the frame of this [...] Read more.
A numerical model to simulate the laser thermoforming process (LTF) is proposed. It is developed on the basis of the thermodynamically consistent theory of coupled thermo-viscoplasticity and is suitable for modeling the LTF for thin-walled metal structural elements. In the frame of this model, the problem statement consists of the Cauchy relation, equations of motion, and the energy balance equation, which is reduced to the heat conduction equation, along with mechanical and thermal boundary conditions, as well as initial conditions. To describe the behavior of the material, a generalized model of physically nonlinear temperature-dependent thermo-viscoplasticity is used. Spatial discretization of the axisymmetric problem of laser pulse loading of the disk is performed by the FEM. The unsteady LTF process of the deformed disk configuration is simulated. The final profile of the disk is obtained as a result of a thermally induced residual stress–strain state caused by the rapid heating and subsequent gradual cooling of the material under the laser-irradiated area. Full article
(This article belongs to the Special Issue Modern Trends and Application of Decision-Making Theory, Stability and Control)
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15 pages, 3864 KiB  
Article
Application of SVM, FFNNs, k-NN and Their Ensembles for Identifying Functionally Reliable Systems
by Oleg Barabash, Andriy Makarchuk, Pavlo Open’ko and Serhii Korotin
Axioms 2025, 14(4), 237; https://doi.org/10.3390/axioms14040237 - 21 Mar 2025
Viewed by 204
Abstract
Active informatization of various spheres of human activity requires increasingly widespread use of information systems. Along with the growing need for their application, the demands on the systems themselves are also rising. Some of these demands can be addressed through technical improvements; however, [...] Read more.
Active informatization of various spheres of human activity requires increasingly widespread use of information systems. Along with the growing need for their application, the demands on the systems themselves are also rising. Some of these demands can be addressed through technical improvements; however, there are aspects for which this alone may not suffice. One such requirement is functional stability. While it is technically possible to ensure functional stability, a number of indicators and criteria have been developed for assessing it. However, applying these indicators in real-world conditions requires significant computational resources. Therefore, there is a need to develop more optimized methods to evaluate whether a system is functionally stable or to improve existing ones. Recently, interest in machine learning methods as a means of optimizing various computations has grown significantly. Accordingly, the question arises as to whether machine learning can be applied to assess the functional stability of information systems. In this study, we investigate the application of some popular classification methods—SVM, FFNNs, k-NN and their ensembles—to determine compliance with one of the requirements for the structure of information systems, which helps evaluate whether the system is functionally stable. Full article
(This article belongs to the Special Issue Modern Trends and Application of Decision-Making Theory, Stability and Control)
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13 pages, 272 KiB  
Article
Application of the Averaging Method to the Optimal Control of Parabolic Differential Inclusions on the Semi-Axis
by Nina Kasimova and Petro Feketa
Axioms 2025, 14(1), 74; https://doi.org/10.3390/axioms14010074 - 20 Jan 2025
Viewed by 698
Abstract
In this paper, we use the averaging method to find an approximate solution for the optimal control of parabolic differential inclusion with fast-oscillating coefficients on a semi-axis. Full article
(This article belongs to the Special Issue Modern Trends and Application of Decision-Making Theory, Stability and Control)
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