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Mathematics
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Finite-Time/Fixed-Time Stability and Control of Dynamical Systems
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Finite-Time/Fixed-Time Stability and Control of Dynamical Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: 30 April 2025 | Viewed by 3879

Special Issue Editors

Prof. Dr. Leimin Wang

E-Mail Website
Guest Editor
School of Automation, China University of Geosciences, Wuhan 430074, China
Interests: memristive systems; dynamics of delayed neural networks; chaotic system encryption; finite-time control
Prof. Dr. Cheng Hu

E-Mail Website
Guest Editor
College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China
Interests: nonlinear complex systems; fractional-order system theory and application; neural networks dynamics and control
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The traditional approach to stability analysis and control design for dynamical systems, often rooted in Lyapunov theory, has proven to be robust and versatile. However, in many modern applications, such as high-speed robotics, aerospace vehicles, and precision manufacturing systems, the requirement for convergence to equilibrium states within a finite time has emerged as a critical performance metric. This necessity has fueled the development of finite-time and fixed-time stability concepts, which offer the promise of faster and more predictable system responses.

The purpose of this Special Issue is to bring together experts from various disciplines, including control engineering, applied mathematics, and computer science, to discuss the latest advancements, challenges, and opportunities in enhancing the stability and control of dynamical systems within finite/fixed-time horizons. The objective is to foster interdisciplinary collaboration, stimulate innovative research, and promote the dissemination of knowledge and best practices in this rapidly evolving field.

We cordially invite researchers, practitioners, and academics working in this exciting area to submit original research articles, review papers, and case studies for consideration to this Special Issue. Contributions should focus on advancing the understanding of finite-time/fixed-time stability and the control of dynamical systems, either through theoretical developments, novel control strategies, or practical implementations. By participating in this Special Issue, contributing authors will have the opportunity to showcase their work to a broad and engaged audience and contribute to the ongoing progress in this critical research field.

Prof. Dr. Leimin Wang
Prof. Dr. Cheng Hu
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. 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

  • finite-time stability
  • fixed-time stability
  • finite-time synchronization
  • fixed-time synchronization
  • neural networks
  • complex networks
  • multi-agent systems
  • time-delay systems
  • control theory
  • control engineering

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Published Papers (5 papers)

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Research

20 pages, 1249 KiB  
Article
Adaptive Approximate Predefined-Time Guaranteed Performance Control of Uncertain Spacecraft
by Liangmou Hu, Zeng Wang, Changrui Chen and Heng Yue
Mathematics 2025, 13(5), 832; https://doi.org/10.3390/math13050832 - 1 Mar 2025
Viewed by 415
Abstract
This brief tackles the predefined-time attitude tracking problem with guaranteed performance for rigid spacecraft subject to uncertain inertia, external disturbances, and actuator partial failure. Firstly, a nonlinear prescribed performance function (NPPF) is constructed, and a non-singular predefined-time terminal sliding mode (NPTSM) surface integrating [...] Read more.
This brief tackles the predefined-time attitude tracking problem with guaranteed performance for rigid spacecraft subject to uncertain inertia, external disturbances, and actuator partial failure. Firstly, a nonlinear prescribed performance function (NPPF) is constructed, and a non-singular predefined-time terminal sliding mode (NPTSM) surface integrating with the NPPF is introduced. Secondly, adaptive non-singular predefined-time guaranteed performance control (ANPTGPC) is designed to tackle the robust attitude tracking problem of rigid spacecraft with predefined-time stability. It is proven that attitude tracking errors can be constrained in the preset tracking performance bound within predefined time. They tend to a small region centered around zero in predefined time and then converge to zero asymptotically. Features of the proposed ANPTGPC include an absence of a model, nonsingularity, predefined-time stability with performance quantified, fast transience, and high steady-state accuracy. Numerical simulation results validate the effectiveness and improved performance of the proposed approach. Full article
(This article belongs to the Special Issue Finite-Time/Fixed-Time Stability and Control of Dynamical Systems)
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20 pages, 4342 KiB  
Article
Distributed Observer-Based Adaptive Formation-Containment Tracking for Multi-Agent Systems on Directed Graphs
by Qi Zhang, Ke-Xing Yan, Bo Xiao and Tao Han
Mathematics 2025, 13(4), 558; https://doi.org/10.3390/math13040558 - 8 Feb 2025
Viewed by 440
Abstract
This article investigates the issue of observer-based adaptive time-varying formation-containment tracking (TVFCT) for multi-agent systems (MASs) with bounded unknown input in directed graphs. By applying estimated statuses of neighboring agents, two observer-based adaptive TVFCT control algorithms are deployed for MASs with multiple tracking [...] Read more.
This article investigates the issue of observer-based adaptive time-varying formation-containment tracking (TVFCT) for multi-agent systems (MASs) with bounded unknown input in directed graphs. By applying estimated statuses of neighboring agents, two observer-based adaptive TVFCT control algorithms are deployed for MASs with multiple tracking leaders and one tracking leader, respectively. Notably, the proposed control algorithms remain independent and do not rely on the comprehensive global information of the entire communication network. Furthermore, the algebraic Riccati inequalities and the Lyapunov theorem provide the bases for assessing the achievement of TVFCT in MASs within directed graphs. Lastly, simulation results are provided to validate the theoretical conclusions. Full article
(This article belongs to the Special Issue Finite-Time/Fixed-Time Stability and Control of Dynamical Systems)
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19 pages, 829 KiB  
Article
Zero-Sum-Game-Based Fixed-Time Event-Triggered Optimal Consensus Control of Multi-Agent Systems Under FDI Attacks
by Jing Yang, Ruihong Li, Qintao Gan and Xinxin Huang
Mathematics 2025, 13(3), 543; https://doi.org/10.3390/math13030543 - 6 Feb 2025
Viewed by 697
Abstract
This paper concentrates on the fixed-time optimal consensus issue of multi-agent systems (MASs) under false data injection (FDI) attacks. To mitigate FDI attacks on sensors and actuators that may cause systems to deviate from the reference trajectory, a zero-sum game framework is established, [...] Read more.
This paper concentrates on the fixed-time optimal consensus issue of multi-agent systems (MASs) under false data injection (FDI) attacks. To mitigate FDI attacks on sensors and actuators that may cause systems to deviate from the reference trajectory, a zero-sum game framework is established, where the secure control protocol aims at the better system performance, yet the attacker plays a contrary role. By solving the Hamilton–Jacobi–Isaacs (HJI) equation related to the zero-sum game, an optimal secure tracking controller based on the event-triggered mechanism (ETM) is obtained to decrease the consumption of system resources while the fixed-time consensus can be guaranteed. Moreover, a critic-only online reinforcement learning (RL) algorithm is proposed to approximate the optimal policy, in which the critic neural networks are constructed by the experience replay-based approach. The unmanned aerial vehicle (UAV) systems are adopted to verify the feasibility of the presented approach. Full article
(This article belongs to the Special Issue Finite-Time/Fixed-Time Stability and Control of Dynamical Systems)
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17 pages, 1370 KiB  
Article
Finite-Time Stability Analysis of a Discrete-Time Generalized Reaction–Diffusion System
by Othman Abdullah Almatroud and Adel Ouannas
Mathematics 2024, 12(23), 3679; https://doi.org/10.3390/math12233679 - 24 Nov 2024
Cited by 1 | Viewed by 915
Abstract
This paper delves into a comprehensive analysis of a generalized impulsive discrete reaction–diffusion system under periodic boundary conditions. It investigates the behavior of reactant concentrations through a model governed by partial differential equations (PDEs) incorporating both diffusion mechanisms and nonlinear interactions. By employing [...] Read more.
This paper delves into a comprehensive analysis of a generalized impulsive discrete reaction–diffusion system under periodic boundary conditions. It investigates the behavior of reactant concentrations through a model governed by partial differential equations (PDEs) incorporating both diffusion mechanisms and nonlinear interactions. By employing finite difference methods for discretization, this study retains the core dynamics of the continuous model, extending into a discrete framework with impulse moments and time delays. This approach facilitates the exploration of finite-time stability (FTS) and dynamic convergence of the error system, offering robust insights into the conditions necessary for achieving equilibrium states. Numerical simulations are presented, focusing on the Lengyel–Epstein (LE) and Degn–Harrison (DH) models, which, respectively, represent the chlorite–iodide–malonic acid (CIMA) reaction and bacterial respiration in Klebsiella. Stability analysis is conducted using Matlab’s LMI toolbox, confirming FTS at equilibrium under specific conditions. The simulations showcase the capacity of the discrete model to emulate continuous dynamics, providing a validated computational approach to studying reaction-diffusion systems in chemical and biological contexts. This research underscores the utility of impulsive discrete reaction-diffusion models for capturing complex diffusion–reaction interactions and advancing applications in reaction kinetics and biological systems. Full article
(This article belongs to the Special Issue Finite-Time/Fixed-Time Stability and Control of Dynamical Systems)
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16 pages, 1381 KiB  
Article
A Martingale Posterior-Based Fault Detection and Estimation Method for Electrical Systems of Industry
by Chao Cheng, Weijun Wang, He Di, Xuedong Li, Haotong Lv and Zhiwei Wan
Mathematics 2024, 12(20), 3200; https://doi.org/10.3390/math12203200 - 12 Oct 2024
Cited by 1 | Viewed by 932
Abstract
The improvement of information sciences promotes the utilization of data for process monitoring. As the core of modern automation, time-stamped signals are used to estimate the system state and construct the data-driven model. Many recent studies claimed that the effectiveness of data-driven methods [...] Read more.
The improvement of information sciences promotes the utilization of data for process monitoring. As the core of modern automation, time-stamped signals are used to estimate the system state and construct the data-driven model. Many recent studies claimed that the effectiveness of data-driven methods relies greatly on data quality. Considering the complexity of the operating environment, process data will inevitably be affected. This poses big challenges to estimating faults from data and delivers feasible strategies for electrical systems of industry. This paper addresses the missing data problem commonly in traction systems by designing a martingale posterior-based data generation method for the state-space model. Then, a data-driven approach is proposed for fault detection and estimation via the subspace identification technique. It is a general scheme using the Bayesian framework, in which the Dirichlet process plays a crucial role. The data-driven method is applied to a pilot-scale traction motor platform. Experimental results show that the method has good estimation performance. Full article
(This article belongs to the Special Issue Finite-Time/Fixed-Time Stability and Control of Dynamical Systems)
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