Advances in Mathematical Optimal Control and Applications

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

Deadline for manuscript submissions: 31 December 2025 | Viewed by 1818

Special Issue Editors


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Guest Editor
Department of Mathematics, Louisiana State University, 303 Lockett Hall, Baton Rouge, LA 70803, USA
Interests: necessary conditions of optimality; impulsive problems; gap phenomena; ODE with time delays; asymptotic controllability; feedback stabilizability; lie brackets; nonsmooth analysis; interval analysis; systems with uncertainty

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Guest Editor
1. The Galilee Research Center for Applied Mathematics, Braude College of Engineering, Karmiel 2161002, Israel
2. Department of Mathematics, Braude College of Engineering, Karmiel 2161002, Israel
Interests: asymptotic methods; differential games; generalized functions; hybrid systems; optimal control; robust control; singular optimal control problems and singular differential games; singularly perturbed problems; stochastic difference and differential equations; systems theory; time delay systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Control theory is a mathematical discipline that deals with the modeling and regulation of dynamical systems, with the goal of guiding their behavior to meet specific objectives. It involves developing strategies to manipulate inputs to achieve desired outputs, ensuring system stability, performance, and efficiency. Control theory is essential in managing uncertainty, disturbances, and fluctuations in systems, making it a powerful tool in various domains.

As systems grow increasingly complex, with applications spanning from engineering and robotics to economics and biology, advancements in control theory become more crucial. New approaches are continually being developed to address challenges in areas such as nonlinear control, adaptive control, and optimal control. These methods aim to enhance system performance in environments with uncertainty and dynamic change.

This Special Issue is dedicated to the latest advancements in control theory, providing a platform for presenting cutting-edge research and developments. The guest editors invite submissions that explore both the theoretical foundations and practical applications of control theory, with a focus on emerging techniques and their applications in modern science and engineering. This issue aims to serve as a valuable resource for researchers and practitioners working to push the boundaries of control theory.

Among the topics that this Special Issue will address, we may consider the following non-exhaustive list: necessary conditions of optimality; sufficient conditions of optimality; maximum principle; control systems with time delays; control of PDE; consensus models; traffic models; adaptive control; impulsive problems; asymptotic controllability; design of feedback laws; control systems with uncertainty; applications of control theory.

We hope that this initiative will be attractive to researchers specialized in the above-mentioned fields. Contributions may be submitted on a continuous basis before the deadline. After a peer-review process, submissions will be selected for publication based on their quality and relevance.

Dr. Giovanni Fusco
Prof. Dr. Valery Y. Glizer
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

  • stabilizability
  • controllability
  • maximum principle
  • feedback controls
  • optimization
  • delay systems
  • robust controls
  • parameter estimation

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Published Papers (3 papers)

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Research

12 pages, 291 KiB  
Article
Optimal Control Problems for Erlang Loss Systems
by Mario Lefebvre
Axioms 2025, 14(2), 130; https://doi.org/10.3390/axioms14020130 - 11 Feb 2025
Viewed by 404
Abstract
An Erlang loss system, which is an M/G/s/s queue, is a model used in various applications. In this paper, a controlled version of the process is defined. The objective is to maximize the expected time until the [...] Read more.
An Erlang loss system, which is an M/G/s/s queue, is a model used in various applications. In this paper, a controlled version of the process is defined. The objective is to maximize the expected time until the system is full when the service time is exponentially distributed. The control variable is the service rate. The dynamic programming equation satisfied by the value function F, from which the optimal control follows at once, is derived, and F is found explicitly when s=2 and s=3. The problem of minimising the probability of the system being saturated is also considered. Full article
(This article belongs to the Special Issue Advances in Mathematical Optimal Control and Applications)
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35 pages, 460 KiB  
Article
Bilinear Optimal Control for a Nonlinear Parabolic Equation Involving Nonlocal-in-Time Term
by Gisèle Mophou, Arnaud Fournier and Célia Jean-Alexis
Axioms 2025, 14(1), 38; https://doi.org/10.3390/axioms14010038 - 4 Jan 2025
Viewed by 541
Abstract
We study a bilinear optimal control problem for an evolution equation with a nonlinear term that depends on both the state and its time integral. First, we establish existence and uniqueness results for this evolution equation. Then, we derive weak maximum principle results [...] Read more.
We study a bilinear optimal control problem for an evolution equation with a nonlinear term that depends on both the state and its time integral. First, we establish existence and uniqueness results for this evolution equation. Then, we derive weak maximum principle results to improve the regularity of the state equation. We proceed by formulating an optimal control problem aimed at steering the system’s state to a desired final state. Finally, we demonstrate that this optimal control problem admits a solution and derive the first- and second-order optimality conditions. Full article
(This article belongs to the Special Issue Advances in Mathematical Optimal Control and Applications)
14 pages, 490 KiB  
Article
About Stabilization of the Controlled Inverted Pendulum Under Stochastic Perturbations of the Type of Poisson’s Jumps
by Leonid Shaikhet
Axioms 2025, 14(1), 29; https://doi.org/10.3390/axioms14010029 - 31 Dec 2024
Viewed by 466
Abstract
The classical problem of stabilization of the controlled inverted pendulum is considered in the case of stochastic perturbations of the type of Poisson’s jumps. It is supposed that stabilized control depends on the entire trajectory of the pendulum. Linear and nonlinear models of [...] Read more.
The classical problem of stabilization of the controlled inverted pendulum is considered in the case of stochastic perturbations of the type of Poisson’s jumps. It is supposed that stabilized control depends on the entire trajectory of the pendulum. Linear and nonlinear models of the controlled inverted pendulum are considered, and the stability of the zero and nonzero equilibria is studied. The obtained results are illustrated by examples with numerical simulation of solutions of the equations under consideration. Full article
(This article belongs to the Special Issue Advances in Mathematical Optimal Control and Applications)
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