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Mathematics
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Recent Advances in Nonlinear Control Theory and System Dynamics
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Recent Advances in Nonlinear Control Theory and System Dynamics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 10 May 2026 | Viewed by 2523

Special Issue Editors

Dr. Zhe Zhang

E-Mail Website
Guest Editor
1. School of Electrical Engineering, Guangxi University, Nanning, China
2. College of Electrical and Information Engineering, Hunan University, Changsha, China
Interests: fractional system dynamics; nonlinear control theory and technology; robot visual perception and control
Special Issues, Collections and Topics in MDPI journals
Dr. Xiaokang Liu

E-Mail Website
Guest Editor
School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China
Interests: smart grid; distributed control and optimization

Special Issue Information

Dear Colleagues, 

With the continuous development of technology, nonlinear phenomena in modern engineering and industrial systems are becoming increasingly prominent. Due to their complex dynamic characteristics, nonlinear systems often exhibit multiple stabilities, chaotic behaviors, and complex dynamic responses; therefore, research on nonlinear control theory and system dynamics becomes particularly important. In recent years, with the improvement of computing power and the continuous development of control theory, significant progress has been made in the research on nonlinear control methods; in particular, many breakthroughs have been achieved in aspects such as robust control, optimal control, adaptive control, and sliding mode control. Nevertheless, the application of nonlinear control theory and system dynamics in practical engineering still faces many challenges, such as system uncertainty, external interference, and model mismatch. Therefore, further promoting research on nonlinear control theory and system dynamics remains the key to achieving efficient, stable, and reliable control systems.

The main purpose of this Special Issue is to gather innovative research achievements in the fields of nonlinear control theory and system dynamics, covering the latest progress in nonlinear theory analysis, system dynamics research, and artificial intelligence-based methods. We welcome you to submit and showcase cutting-edge research achievements in nonlinear system modeling, stability analysis, control strategy design, and dynamic behavior prediction. We encourage in-depth discussions on control methods in multi-scale, nonlinear coupled systems and complex environments, as well as the design of control strategies based on artificial intelligence, to promote the interdisciplinary integration and innovative application of nonlinear control theory and system dynamics.

Dr. Zhe Zhang
Dr. Xiaokang Liu
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. 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

  • dynamics modeling and analysis of nonlinear systems
  • nonlinear control theory
  • stability analysis
  • analysis and control of fractional systems
  • chaos control and synchronization
  • system stability and performance optimization
  • robot control theory
  • multiphysics field coupling control
  • artificial intelligence-driven control theory

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Published Papers (3 papers)

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Research

17 pages, 38037 KB  
Article
Wide Voltage Gain Range for Auxiliary Half-Bridge Dual Active Bridge Converter Between Electric Vehicles Based on Nonlinear Virtual Power Predictive Control
by Yuhan Guo, Wentao Yang and Zhenao Sun
Mathematics 2026, 14(7), 1155; https://doi.org/10.3390/math14071155 - 30 Mar 2026
Viewed by 332
Abstract
Although electric vehicles are being vigorously promoted around the world, the mileage anxiety problem is an important hindrance to their development. Thus, this paper proposes an auxiliary half-bridge dual active bridge (AH-DAB) converter between different electric vehicles, which is based on nonlinear virtual [...] Read more.
Although electric vehicles are being vigorously promoted around the world, the mileage anxiety problem is an important hindrance to their development. Thus, this paper proposes an auxiliary half-bridge dual active bridge (AH-DAB) converter between different electric vehicles, which is based on nonlinear virtual power predictive control. For the converter, characteristics of high power density, wide voltage gain range, and high efficiency are necessary. Firstly, an AH-DAB converter is applied to improve the control variable. Under this effect, the converter can switch between the half-bridge and the full-bridge converter. Secondly, a duty ratio design method is proposed to improve zero-voltage switching (ZVS) performance. Therefore, wide voltage gain range, decoupling of control variables, and high efficiency can be achieved in the nonlinear AH-DAB system. Thirdly, the nonlinear virtual power predictive control is proposed to ensure energy transfer between two electric vehicles. Based on this, the phase shift angle can be predicted and adjusted by ensuring that the actual power is consistently maintained close to the reference power. Moreover, the virtual power is generated to represent the reference power, which can reduce the number of current sensors. Finally, simulation and experiment results collectively show the wide voltage gain range and high efficiency of the proposed AH-DAB converter. Full article
(This article belongs to the Special Issue Recent Advances in Nonlinear Control Theory and System Dynamics)
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23 pages, 20415 KB  
Article
Nonlinear Dynamics of Discrete-Time Model for Computer Virus Propagation: Chaos, Complexity, Stabilization and Synchronization
by Ali Aloui, Imane Zouak, Omar Kahouli, Adel Ouannas, Lilia El Amraoui and Mohamed Ayari
Mathematics 2025, 13(22), 3681; https://doi.org/10.3390/math13223681 - 17 Nov 2025
Cited by 1 | Viewed by 492
Abstract
This paper investigates a discrete-time compartmental model for computer virus propagation. The model classifies computers into susceptible, latent, and breaking-out states, with nonlinear dynamics driven by infection, recovery, and breakout processes. Stability is analyzed using the basic reproduction number R0, and [...] Read more.
This paper investigates a discrete-time compartmental model for computer virus propagation. The model classifies computers into susceptible, latent, and breaking-out states, with nonlinear dynamics driven by infection, recovery, and breakout processes. Stability is analyzed using the basic reproduction number R0, and chaotic behavior is demonstrated through phase portraits, bifurcation diagrams, and maximum Lyapunov exponents. To further characterize complexity, the C0 complexity measure is computed, confirming the richness of the chaotic regime. In addition, control strategies are designed to stabilize the dynamics, and a master–slave synchronization scheme is proposed and validated. Numerical simulations highlight both the complexity and controllability of the system, underscoring its relevance for understanding and mitigating the propagation of computer viruses. Full article
(This article belongs to the Special Issue Recent Advances in Nonlinear Control Theory and System Dynamics)
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20 pages, 2798 KB  
Article
Adaptive Fuzzy Fault-Tolerant Formation Control of High-Order Fully Actuated Multi-Agent Systems with Time-Varying Delays
by Yang Cui and Kaichao Liu
Mathematics 2025, 13(17), 2813; https://doi.org/10.3390/math13172813 - 1 Sep 2025
Cited by 2 | Viewed by 756
Abstract
The adaptive fuzzy fault-tolerant formation control of nonlinear high-order fully actuated multi-agent systems is studied in this paper, which contains time-varying delays and nonlinear non-affine faults. In contrast to the state-space approach, the proposed control method is based on the fully actuated system [...] Read more.
The adaptive fuzzy fault-tolerant formation control of nonlinear high-order fully actuated multi-agent systems is studied in this paper, which contains time-varying delays and nonlinear non-affine faults. In contrast to the state-space approach, the proposed control method is based on the fully actuated system approach, which does not require converting a high-order system into a first-order one but directly designs controllers for high-order nonlinear multi-agent systems. The time-varying delays of the systems can be solved using the finite covering lemma and fuzzy logic systems. Compared with the traditional Lyapunov–Krasovskii functional method, the proposed control methodology relaxes the constraint of bounded derivatives for time-varying delays. The problem of algebraic loop in controller design caused by nonlinear non-affine faults is avoided using a Butterworth low-pass filter. Based on the Lyapunov stability theory, the proposed controller methodology is demonstrated to ensure the stability of the closed-loop system, and all followers can keep ideal formation with the leader. Finally, the validity of the theoretical results is demonstrated through three simulation examples, and the design steps of the controller for the simulation examples are reduced by fifty percent compared to the state-space method. Full article
(This article belongs to the Special Issue Recent Advances in Nonlinear Control Theory and System Dynamics)
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