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Symmetry
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Symmetry in Optimal Control and Applications
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Symmetry in Optimal Control and Applications

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 30 September 2025 | Viewed by 1130

Special Issue Editors

Dr. Xin Chen

E-Mail Website
Guest Editor
College of Science, Nanjing Forestry University, Nanjing 210037, China
Interests: machine learning; optimal control theory; game theory
Dr. Liu He

E-Mail Website
Guest Editor
College of Science, Nanjing Forestry University, Nanjing 210037, China
Interests: uncertain statistics; fractional dynamic system; parameter estimation
Dr. Bo Li

E-Mail Website
Guest Editor
School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, China
Interests: portfolio selection; uncertain optimization; optimal control
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Optimal control theory is a fundamental area of mathematics that has profound implications across numerous disciplines, including engineering, economics, biology, and more. By providing a framework for determining control strategies that optimize a given performance criterion, optimal control has become an essential tool for solving complex real-world problems. The aim of this Special Issue is to attract leading researchers in these areas in order to include new high-quality results involving their symmetry properties, both from a theoretical and an applied point of view. All articles related to optimal control theory are invited to be submitted for this Special Issue.

The topics of interest for this Special Issue include but are not limited to the following:

  • Uncertain optimal control and application;
  • Adaptive and robust control strategies;
  • Control of distributed and networked systems;
  • Applications of optimal control in robotics and autonomous systems;
  • Optimal control in biological and medical systems;
  • Fractional systems and its applications;
  • Financial models and economic systems;
  • Energy management and optimization;
  • Computational methods for solving optimization problems;
  • Multi-agent and distributed control systems.

Dr. Xin Chen
Dr. Liu He
Dr. Bo Li
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. Symmetry 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
  • robust control
  • uncertainty theory
  • computational methods
  • applications in robotics
  • fractional systems
  • biological systems
  • economic systems
  • energy optimization
  • symmetry in financial models and economic systems

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Published Papers (2 papers)

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Research

19 pages, 1771 KiB  
Article
A New Adaptive Control Design of Permanent Magnet Synchronous Motor Systems with Uncertainties
by Yutang Liu, Jiaojiao Li, Zong-Yao Sun and Chih-Chiang Chen
Symmetry 2025, 17(1), 2; https://doi.org/10.3390/sym17010002 - 24 Dec 2024
Abstract
Symmetry is widely present in science and daily life. And the internal structure of surface-mounted permanent magnet synchronous motors (PMSMs) has good symmetry. This article is dedicated to studying the tracking problem of PMSMs with adaptive and backstepping control methods. The research objective [...] Read more.
Symmetry is widely present in science and daily life. And the internal structure of surface-mounted permanent magnet synchronous motors (PMSMs) has good symmetry. This article is dedicated to studying the tracking problem of PMSMs with adaptive and backstepping control methods. The research objective of this study is to design new adaptive controllers Uq and Ud, which enable the state of the motor position servo system to asymptotically and stably track the given signals of the system. They can suppress the impact of changes in B, J, and TL and can also enhance the robustness of the system. (i) The strongly coupled current and speed, variation of parameters over time, and nonlinearity of motor torque objectively pose significant challenges in the design of adaptive tracking controllers for PMSMs. (ii) Adaptive control technology and backstepping control methods are used for designing controllers for the PMSMs. (iii) After rigorous reasoning, an intelligent adaptive tracking control strategy for the PMSMs has been derived, which is for the direct axis current and the angle. (iv) The new adaptive tracking controllers are superior to existing controllers in that they can strongly suppress the disturbance of system parameters J, TL, and B, make the system state asymptotically stable, and achieve good tracking performance for the given signals. The results of the simulation indicate the validity of the designed control strategy. Full article
(This article belongs to the Special Issue Symmetry in Optimal Control and Applications)
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11 pages, 277 KiB  
Article
A New Method of Teaching Quality Evaluation Based on the α-Pessimistic Shapley Value
by Yin Gao
Symmetry 2024, 16(11), 1556; https://doi.org/10.3390/sym16111556 - 20 Nov 2024
Viewed by 595
Abstract
Coalitional game with uncertain payoffs driven by uncertain variables stands for uncertain coalitional game. A α-pessimistic Shapley value as the solution of uncertain coalitional game is proposed in this paper, which can be played an important role in solving the problem of [...] Read more.
Coalitional game with uncertain payoffs driven by uncertain variables stands for uncertain coalitional game. A α-pessimistic Shapley value as the solution of uncertain coalitional game is proposed in this paper, which can be played an important role in solving the problem of profit allocation. Moreover, the α-pessimistic Shapley value is proved to be the only value satisfying symmetry, dummy and additivity. Based on the α-pessimistic Shapley value, a new method of teaching quality evaluation in the institutions of higher learning is presented. In order to obtain the index of teaching quality evaluation in uncertain environments, an α-pessimistic multilinear extension is defined. Meanwhile, some properties of α-pessimistic multilinear extension are investigated successfully. Moreover, the problem of teaching quality evaluation are considered in this paper. Full article
(This article belongs to the Special Issue Symmetry in Optimal Control and Applications)
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