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Axioms
Special Issues
Recent Developments in Stability and Control of Dynamical Systems
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Recent Developments in Stability and Control of Dynamical Systems

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 31 January 2025 | Viewed by 3824

Special Issue Editors

Dr. Shengda Zeng

E-Mail Website
Guest Editor
Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, China
Interests: nonlinear analysis; fractional calculus; partial differential equations; nonsmooth analysis; control theory; variational/hemivariational inequalities; numerical analysis; contact mechanics problems; fluid mechanics problems; mathematical modelling; applied mathematics; fuzzy mathematics; stability analysis; convergence analysis
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Stanisław Migórski

E-Mail Website
Guest Editor
Faculty of Mathematics and Computer Science, Jagiellonian University, 30348 Krakow, Poland
Interests: differential equations; nonlinear functional analysis; methods and techniques of nonlinear analysis; calculus of variations; control theory; identification; homogenization; mathematical modeling of physical systems; applications of PDEs to problems of mechanics

Special Issue Information

Dear Colleagues,

Mathematical modeling is an essential tool in studying a diverse range of dynamical systems. It describes the behaviors of complex and nonlinear phenomena in mathematics and physics, but it also has a long and rich tradition of applications in engineering, biology, economics, statistics, etc. In real-world problems, mathematical modeling of dynamical system is largely based on the abstraction that information is transmitted along perfect communication channels and that computation is either instantaneous (continuous-time) or periodic (discrete-time). In principle, there are two major sources of error in modelling of physical events: approximation errors due to the inherent inaccuracies incurred in the discretization of the events and modeling errors due to the natural imperfections in abstract models of actual physical phenomena. In order to deal with these issues, sophisticated mathematical techniques are needed. On the other hand, the important properties of dynamical systems play a central role in control systems. The stability concept is essential, because almost every practical control system is designed to be stable.

The objective of this Special Issue is to compile recent developments in methodologies and techniques for stability and control design of dynamical systems to deal with issues such as nonlinear events, kinematics of the actuators, reliability and security of communications, bandwidth allocation, development of data communication protocols, fault detection and fault tolerant control, real-time information collection, and efficient processing of sensor data. Relevant topics include, but are not limited to, the following areas:

  • Stability and control design;
  • Qualitative behaviors of dynamical systems;
  • Linear and nonlinear system modeling;
  • Stochastic dynamical systems;
  • Fuzzy systems and its applications;
  • Networked control systems.

Dr. Shengda Zeng
Prof. Dr. Stanisław Migórski
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

  • optimal control
  • differential equations and differential inclusions
  • stability
  • sensitivity
  • optimal conditions
  • fuzzy systems
  • variational analysis
  • numerical analysis
  • qualitative analysis
  • shape optimization

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Published Papers (6 papers)

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Research

17 pages, 334 KiB  
Article
A Penalty Method for Elliptic Variational–Hemivariational Inequalities
by Mircea Sofonea and Domingo A. Tarzia
Axioms 2024, 13(10), 721; https://doi.org/10.3390/axioms13100721 - 17 Oct 2024
Viewed by 216
Abstract
We consider an elliptic variational–hemivariational inequality P in a real reflexive Banach space, governed by a set of constraints K. Under appropriate assumptions of the data, this inequality has a unique solution u∈K. We associate inequality P to a [...] Read more.
We consider an elliptic variational–hemivariational inequality P in a real reflexive Banach space, governed by a set of constraints K. Under appropriate assumptions of the data, this inequality has a unique solution u∈K. We associate inequality P to a sequence of elliptic variational–hemivariational inequalities {Pn}, governed by a set of constraints K˜⊃K, a sequence of parameters {λn}⊂R+, and a function ψ. We prove that if, for each n∈N, the element un∈K˜ represents a solution to Problem Pn, then the sequence {un} converges to u as λn→0. Based on this general result, we recover convergence results for various associated penalty methods previously obtained in the literature. These convergence results are obtained by considering particular choices of the set K˜ and the function ψ. The corresponding penalty methods can be applied in the study of various inequality problems. To provide an example, we consider a purely hemivariational inequality that describes the equilibrium of an elastic membrane in contact with an obstacle, the so-called foundation. Full article
(This article belongs to the Special Issue Recent Developments in Stability and Control of Dynamical Systems)
15 pages, 283 KiB  
Article
Sufficient Efficiency Criteria for New Classes of Non-Convex Optimization Models
by Savin Treanţă and Omar Mutab Alsalami
Axioms 2024, 13(9), 572; https://doi.org/10.3390/axioms13090572 - 23 Aug 2024
Viewed by 376
Abstract
In this paper, we introduce and study a new class of minimization models driven by multiple integrals as cost functionals. Concretely, we formulate and establish some sufficient efficiency criteria for a feasible point in the considered optimization problem. To this end, we introduce [...] Read more.
In this paper, we introduce and study a new class of minimization models driven by multiple integrals as cost functionals. Concretely, we formulate and establish some sufficient efficiency criteria for a feasible point in the considered optimization problem. To this end, we introduce and define the concepts of (Γ,ψ)-invexity and generalized (Γ,ψ)-invexity for the involved real-valued controlled multiple integral-type functionals. More precisely, we extend the notion of (generalized) (Γ,ψ)-invexity to the multiple objective control models driven by multiple integral functionals. In addition, innovative proofs are considered for the principal results derived in the paper. Full article
(This article belongs to the Special Issue Recent Developments in Stability and Control of Dynamical Systems)
13 pages, 2022 KiB  
Article
Advanced Methods for Conformable Time-Fractional Differential Equations: Logarithmic Non-Polynomial Splines
by Majeed A. Yousif, Ravi P. Agarwal, Pshtiwan Othman Mohammed, Alina Alb Lupas, Rashid Jan and Nejmeddine Chorfi
Axioms 2024, 13(8), 551; https://doi.org/10.3390/axioms13080551 - 13 Aug 2024
Cited by 1 | Viewed by 616
Abstract
In this study, we present a numerical method named the logarithmic non-polynomial spline method. This method combines conformable derivative, finite difference, and non-polynomial spline techniques to solve the nonlinear inhomogeneous time-fractional Burgers–Huxley equation. The developed numerical scheme is characterized by a sixth-order convergence [...] Read more.
In this study, we present a numerical method named the logarithmic non-polynomial spline method. This method combines conformable derivative, finite difference, and non-polynomial spline techniques to solve the nonlinear inhomogeneous time-fractional Burgers–Huxley equation. The developed numerical scheme is characterized by a sixth-order convergence and conditional stability. The accuracy of the method is demonstrated with 3D mesh plots, while the effects of time and fractional order are shown in 2D plots. Comparative evaluations with the cubic B-spline collocation method are provided. To illustrate the suitability and effectiveness of the proposed method, two examples are tested, with the results are evaluated using L2 and L∞ norms. Full article
(This article belongs to the Special Issue Recent Developments in Stability and Control of Dynamical Systems)
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10 pages, 262 KiB  
Article
On a Neumann Problem with an Intrinsic Operator
by Dumitru Motreanu and Angela Sciammetta
Axioms 2024, 13(8), 497; https://doi.org/10.3390/axioms13080497 - 25 Jul 2024
Viewed by 345
Abstract
This paper investigates the existence and location of solutions for a Neumann problem driven by a (p,q) Laplacian operator and with a reaction term that depends not only on the solution and its gradient but also incorporates an intrinsic [...] Read more.
This paper investigates the existence and location of solutions for a Neumann problem driven by a (p,q) Laplacian operator and with a reaction term that depends not only on the solution and its gradient but also incorporates an intrinsic operator, which is its main novelty. This paper can be seen as the study of a quasilinear Neumann problem involving an elaborated perturbation with a Nemytskij operator. The approach proceeds through a version of the sub/supersolution method, exploiting an invariance property regarding the sub/supersolution ordered interval with respect to the intrinsic operator. An example illustrates the applicability of our result. Full article
(This article belongs to the Special Issue Recent Developments in Stability and Control of Dynamical Systems)
17 pages, 774 KiB  
Article
Precise Obstacle Avoidance Movement for Three-Wheeled Mobile Robots: A Modified Curvature Tracking Method
by Xiangrong Wen and Yusheng Zhou
Axioms 2024, 13(6), 389; https://doi.org/10.3390/axioms13060389 - 8 Jun 2024
Viewed by 756
Abstract
This paper proposes a precise motion control strategy for a three-wheeled mobile robot with two driven rear wheels and one steered front wheel so that an obstacle avoidance motion task is able to be well implemented. Initially, the motion laws under nonholonomic constraints [...] Read more.
This paper proposes a precise motion control strategy for a three-wheeled mobile robot with two driven rear wheels and one steered front wheel so that an obstacle avoidance motion task is able to be well implemented. Initially, the motion laws under nonholonomic constraints are expounded for the three-wheeled mobile robot in order to facilitate the derivation of its dynamic model. Subsequently, a prescribed target curve is converted into a speed target through the nonholonomic constraint of zero lateral speed. A modified dynamical tracking target that is aligned with the dynamic model is then developed based on the relative curvature of the prescribed curve. By applying this dynamical tracking target, path tracking precision is enhanced through appropriate selection of a yaw motion speed target, thus preventing speed errors from accumulating during relative curvature tracking. On this basis, integral sliding mode control and feedback linearization methods are adopted for designing robust controllers, enabling the accurate movement of the three-wheeled mobile robot along a given path. A theoretical analysis and simulation results corroborate the effectiveness of the proposed trajectory tracking control strategy in preventing off-target deviations, even with significant speed errors. Full article
(This article belongs to the Special Issue Recent Developments in Stability and Control of Dynamical Systems)
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16 pages, 391 KiB  
Article
Exponential Stability of Dynamical Systems on Time Scales with Application to Multi-Agent Systems
by Mingshuo Liu and Huizhe Shi
Axioms 2024, 13(2), 100; https://doi.org/10.3390/axioms13020100 - 31 Jan 2024
Viewed by 1023
Abstract
The exponential stability criteria of systems with time delays on time scales are established, which unifies and generalizes the continuous and discrete cases. The time derivatives of Lyapunov functions (functionals) along solutions are allowed to be indefinite, namely, to take both negative and [...] Read more.
The exponential stability criteria of systems with time delays on time scales are established, which unifies and generalizes the continuous and discrete cases. The time derivatives of Lyapunov functions (functionals) along solutions are allowed to be indefinite, namely, to take both negative and positive value, which reduces conservatism of the criteria. Moreover, the stability criteria are applicable to both linear and nonlinear systems on time scales, which expands the scope of application of the criteria. Furthermore, the improved stability theorem is applied to solve a leader-following consensus problem of multi-agents on time scales. Sufficient conditions are derived for the leader-following consensus of multi-agent systems under directed interaction topology. A numerical example is given to illustrate the feasibility and effectiveness of the theoretical results. Full article
(This article belongs to the Special Issue Recent Developments in Stability and Control of Dynamical Systems)
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