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Symmetry
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Symmetry in Control Systems: Theory, Design, and Application
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Symmetry in Control Systems: Theory, Design, and Application

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

Deadline for manuscript submissions: 31 August 2026 | Viewed by 1621

Special Issue Editors

Dr. Yongfeng Lv

E-Mail Website
Guest Editor
School of Electrical and Power Engineering, Taiyuan University of Technology, Taiyuan, China
Interests: adaptive dynamic programming; reinforcement learning; optimal control
Prof. Dr. Jun Zhao

E-Mail Website
Guest Editor
College of Transportation, Shandong University of Science and Technology, Qingdao 266590, China
Interests: adaptive control; optimal control

Special Issue Information

Dear Colleagues,

This Special Issue is dedicated to the exploration of symmetry as a foundational principle in the control of dynamic systems. Symmetry properties offer powerful methods for model reduction, structural analysis, and the synthesis of control laws, leading to more efficient and robust designs. We seek high-quality contributions that address recent advances in the theory of symmetric control systems, including geometric, algebraic, and structure-preserving approaches. Furthermore, we encourage submissions that address the design of novel control algorithms and their applications in diverse fields such as robotics, autonomous vehicles, power networks, and quantum engineering. This Special Issue aims to highlight how leveraging symmetry can bridge theoretical depth with practical innovation, fostering new solutions to complex engineering challenges. We welcome the submission of original research and review articles.

Dr. Yongfeng Lv
Prof. Dr. Jun Zhao
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 250 words) can be sent to the Editorial Office for assessment.

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

  • symmetry in control
  • geometric mechanics
  • lie groups and algebras
  • nonlinear control systems
  • optimal control
  • adaptive control
  • networked systems
  • motion planning and control
  • hamiltonian systems
  • distributed control

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

Published Papers (3 papers)

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Research

24 pages, 3110 KB  
Article
Adaptive Event-Triggered Dynamic Consensus-Based Distributed Secondary Control Strategy for DC Microgrids
by Yihe Feng, Wuhui Chen and Gengwu Zhang
Symmetry 2026, 18(5), 788; https://doi.org/10.3390/sym18050788 - 5 May 2026
Viewed by 197
Abstract
This paper addresses issues in islanded DC microgrids, including voltage deviation, inaccurate current sharing, and high communication burden, by proposing a distributed secondary control strategy that integrates a dynamic consensus algorithm with an adaptive event-triggered mechanism. Within a hierarchical control framework, the secondary [...] Read more.
This paper addresses issues in islanded DC microgrids, including voltage deviation, inaccurate current sharing, and high communication burden, by proposing a distributed secondary control strategy that integrates a dynamic consensus algorithm with an adaptive event-triggered mechanism. Within a hierarchical control framework, the secondary layer employs an improved dynamic consensus algorithm to estimate the average voltage and proportional current through information exchange among neighboring nodes. Corresponding voltage and current compensations are designed to mitigate voltage droop and ensure accurate proportional sharing of load currents. In this study, a 100 V power supply is stepped down to 47.4 V following primary control. Then, by employing the secondary controller with the proposed algorithm, the voltage is precisely restored to the desired value of 48 V. To further reduce the communication burden, a dynamic event-triggered condition is intended for the output current of each power source, enabling communication and control updates only when the state changes significantly. This approach substantially reduces redundant data transmission and the frequency of controller actions. The positions of the triggering points under the action of the event trigger are also illustrated in the corresponding figures in the following sections. The positions of the triggering points under the action of the event trigger are illustrated in the corresponding figures in the following sections. While communication is accomplished, the voltage remains stable at 48 V. Furthermore, the currents of each distributed unit are stabilized around 6.4 A, satisfying the 1:1:1 current-sharing setting. The asymptotic stability of the closed-loop system is proven based on Lyapunov theory, and Zeno behavior is effectively avoided. Simulation results demonstrate that the proposed strategy achieves rapid voltage restoration and high-precision current sharing under scenarios such as load transients and plug-and-play operations while significantly reducing communication frequency and enhancing system economy and reliability. Full article
(This article belongs to the Special Issue Symmetry in Control Systems: Theory, Design, and Application)
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21 pages, 2215 KB  
Article
Optimal Consensus Tracking Control for Nonlinear Multi-Agent Systems via Actor–Critic Reinforcement Learning
by Yi Mo, Xinsuo Li, Kunyu Xiang and Dengguo Xu
Symmetry 2026, 18(4), 691; https://doi.org/10.3390/sym18040691 - 21 Apr 2026
Viewed by 379
Abstract
This paper presents an adaptive optimal consensus tracking control scheme for canonical nonlinear multi-agent systems (MASs) with unknown dynamics, employing an actor–critic reinforcement learning (RL) framework. The scheme integrates a sliding mode mechanism to suppress tracking errors and ensure consensus tracking between the [...] Read more.
This paper presents an adaptive optimal consensus tracking control scheme for canonical nonlinear multi-agent systems (MASs) with unknown dynamics, employing an actor–critic reinforcement learning (RL) framework. The scheme integrates a sliding mode mechanism to suppress tracking errors and ensure consensus tracking between the followers and the leader. Additionally, optimal control is designed to find a Nash equilibrium in a graphical game. To address the intractability of obtaining an analytical solution for the coupled Hamilton–Jacobi–Bellman (HJB) equation, a policy iteration algorithm is utilized. Within this algorithm, a critic neural network (NN) approximates the gradient of the optimal value function, while an actor NN approximates the optimal control policy. Together, these networks form a compact actor–critic (AC) architecture that achieves optimal consensus tracking. Furthermore, the proposed method guarantees the boundedness of all closed-loop signals while ensuring consensus tracking. Finally, two simulations are conducted to verify the effectiveness and advantages of the proposed method. Full article
(This article belongs to the Special Issue Symmetry in Control Systems: Theory, Design, and Application)
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22 pages, 3685 KB  
Article
Neuro-Adaptive Finite-Time Command-Filter Backstepping Control of Full State Feedback Nonlinear System
by Jiaxun Che, Mengxuan Zhang and Lin Sun
Symmetry 2026, 18(2), 274; https://doi.org/10.3390/sym18020274 - 31 Jan 2026
Viewed by 493
Abstract
This work develops a neuro-adaptive finite-time command-filtered backstepping (CFB) control framework for full-state feedback systems. The design methodology initiates with error transformation techniques to embed finite-time prescribed performance (FT-PP) specifications into the control architecture. Building upon this foundation, a dynamic error compensation system [...] Read more.
This work develops a neuro-adaptive finite-time command-filtered backstepping (CFB) control framework for full-state feedback systems. The design methodology initiates with error transformation techniques to embed finite-time prescribed performance (FT-PP) specifications into the control architecture. Building upon this foundation, a dynamic error compensation system is formulated to neutralize filtering artifacts induced by the finite-time command filter (FT-CF), thereby achieving precise finite-time convergence. To address state estimation requirements, we construct a neural network-based state estimation framework utilizing radial basis function neural networks (RBFNNs) for simultaneous uncertainty approximation and unmeasurable state reconstruction. The synthesis of FT-PP constraints and neural state estimation culminates in the derivation of an adaptive control law with Lyapunov-stable update rules, theoretically ensuring tracking errors enter and remaining within small neighborhoods of target compact sets within predefined finite time horizons. The simulation experiments cover both numerical simulation and actual case studies, which verify the feasibility and effectiveness of the proposed control mode. Full article
(This article belongs to the Special Issue Symmetry in Control Systems: Theory, Design, and Application)
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