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Mathematics
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Analysis and Applications of Control Systems Theory
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Analysis and Applications of Control Systems Theory

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 31 December 2025 | Viewed by 2486

Special Issue Editor

Dr. Quan-Yong Fan

E-Mail Website
Guest Editor
Northwestern Polytechnical University, Xi'an 710071, China
Interests: stochastic; fault tolerant control; adaptive control; actuators; controller design; fault tolerance; linear systems; optimal control; robustness; robust control

Special Issue Information

Dear Colleagues,

The current state of control systems development is marked by significant advancements in technology and theory. From the early analog systems to today’s digital and intelligent controllers, control theory has transformed, adapting to the evolving complexities of modern applications. This evolution has been enabled by advancements in computing power, algorithm design, and the integration of AI and machine learning.

This Special Issue, titled “Analysis and Applications of Control Systems Theory”, presents a specific platform for exploring the latest theoretical advancements and practical implementations in advanced control theory. This theme highlights the critical role of control theory in driving innovation across various fields, including robotics, aerospace, and energy management.

We invite submissions that delve into the following areas of research: advanced control methods for complex systems, the integration of AI and machine learning in control systems, optimization techniques for control system design, the security control of network control systems, and case studies and applications that demonstrate the practical impact of control systems theory.

By showcasing cutting-edge research and applications, this Special Issue aims to foster academic exchanges, promote the development of control systems theory, and facilitate innovative applications in real-world scenarios.

Dr. Quan-Yong Fan
Guest Editor

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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • robust control
  • optimal control
  • adaptive control
  • fault-tolerant control
  • fault detection
  • switching control
  • event-triggered control
  • adaptive dynamic programming
  • security control
  • cyber–physical systems

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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

17 pages, 2483 KiB  
Article
Robust Closed–Open Loop Iterative Learning Control for MIMO Discrete-Time Linear Systems with Dual-Varying Dynamics and Nonrepetitive Uncertainties
by Yawen Zhang, Yunshan Wei, Zuxin Ye, Shilin Liu, Hao Chen, Yuangao Yan and Junhong Chen
Mathematics 2025, 13(10), 1675; https://doi.org/10.3390/math13101675 - 20 May 2025
Abstract
Iterative learning control (ILC) typically requires strict repeatability in initial states, trajectory length, external disturbances, and system dynamics. However, these assumptions are often difficult to fully satisfy in practical applications. While most existing studies have achieved limited progress in relaxing either one or [...] Read more.
Iterative learning control (ILC) typically requires strict repeatability in initial states, trajectory length, external disturbances, and system dynamics. However, these assumptions are often difficult to fully satisfy in practical applications. While most existing studies have achieved limited progress in relaxing either one or two of these constraints simultaneously, this work aims to eliminate the restrictions imposed by all four strict repeatability conditions in ILC. For general finite-duration multi-input multi-output (MIMO) linear discrete-time systems subject to multiple non-repetitive uncertainties—including variations in initial states, external disturbances, trajectory lengths, and system dynamics—an innovative open- closed loop robust iterative learning control law is proposed. The feedforward component is used to make sure the tracking error converges as expected mathematically, while the feedback control part compensates for missing tracking data from previous iterations by utilizing real-time tracking information from the current iteration. The convergence analysis employs an input-to-state stability (ISS) theory for discrete parameterized systems. Detailed explanations are provided on adjusting key parameters to satisfy the derived convergence conditions, thereby ensuring that the anticipated tracking error will eventually settle into a compact neighborhood that meets the required standards for robustness and convergence speed. To thoroughly assess the viability of the proposed ILC framework, computer simulations effectively illustrate the strategy’s effectiveness. Further simulation on a real system, a piezoelectric motor system, verifies that the ILC tracking error converges to a small neighborhood in the sense of mathematical expectation. Extending the ILC to complex real-world applications provides new insights and approaches. Full article
(This article belongs to the Special Issue Analysis and Applications of Control Systems Theory)
21 pages, 1565 KiB  
Article
Preview-Based Optimal Control for Trajectory Tracking of Fully-Actuated Marine Vessels
by Xiaoling Liang, Jiang Wu, Hao Xie and Yanrong Lu
Mathematics 2024, 12(24), 3942; https://doi.org/10.3390/math12243942 - 14 Dec 2024
Viewed by 852
Abstract
In this paper, the problem of preview optimal control for second-order nonlinear systems for marine vessels is discussed on a fully actuated dynamic model. First, starting from a kinematic and dynamic model of a three-degrees-of-freedom (DOF) marine vessel, we derive a fully actuated [...] Read more.
In this paper, the problem of preview optimal control for second-order nonlinear systems for marine vessels is discussed on a fully actuated dynamic model. First, starting from a kinematic and dynamic model of a three-degrees-of-freedom (DOF) marine vessel, we derive a fully actuated second-order dynamic model that involves only the ship’s position and yaw angle. Subsequently, through the higher-order systems methodology, the nonlinear terms in the system were eliminated, transforming the system into a one-order parameterized linear system. Next, we designed an internal model compensator for the reference signal and constructed a new augmented error system based on this compensator. Then, using optimal control theory, we designed the optimal preview controller for the parameterized linear system and the corresponding feedback parameter matrices, which led to the preview controller for the original second-order nonlinear system. Finally, a numerical simulation indicates that the controller designed in this paper is highly effective. Full article
(This article belongs to the Special Issue Analysis and Applications of Control Systems Theory)
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26 pages, 782 KiB  
Article
Recovery Model of Electric Power Data Based on RCNN-BiGRU Network Optimized by an Accelerated Adaptive Differential Evolution Algorithm
by Yukun Xu, Yuwei Duan, Chang Liu, Zihan Xu and Xiangyong Kong
Mathematics 2024, 12(17), 2686; https://doi.org/10.3390/math12172686 - 29 Aug 2024
Viewed by 888
Abstract
Time-of-use pricing of electric energy, as an important part of the national policy of energy conservation and emission reduction, requires accurate electric energy data as support. However, due to various reasons, the electric energy data are often missing. To address this thorny problem, [...] Read more.
Time-of-use pricing of electric energy, as an important part of the national policy of energy conservation and emission reduction, requires accurate electric energy data as support. However, due to various reasons, the electric energy data are often missing. To address this thorny problem, this paper constructs a CNN and GRU-based recovery model (RCNN-BiGRU) for electric energy data by taking the missing data as the output and the historical data of the neighboring moments as the input. Firstly, a convolutional network with a residual structure is used to capture the local dependence and periodic patterns of the input data, and then a bidirectional GRU network utilizes the extracted potential features to model the temporal relationships of the data. Aiming at the difficult selection of network structure parameters and training process parameters, an accelerated adaptive differential evolution (AADE) algorithm is proposed to optimize the electrical energy data recovery model. The algorithm designs an accelerated mutation operator and at the same time adopts an adaptive strategy to set the two key parameters. A large amount of real grid data are selected as samples to train the network, and the comparison results verify that the proposed combined model outperforms the related CNN and GRU networks. The comparison experimental results with other optimization algorithms also show that the AADE algorithm proposed in this paper has better data recovery performance on the training set and significantly better performance on the test set. Full article
(This article belongs to the Special Issue Analysis and Applications of Control Systems Theory)
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