Predefined time synchronization of fractional order chaotic system via sliding mode control

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-09-22 DOI:10.1016/j.cnsns.2025.109332

Feng-Xian Wang , Jun-Qi Cui , Rui-Dong Chen , Xin-Ge Liu

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引用次数: 0

Abstract

In this paper, the predefined time sliding mode control of Caputo fractional order chaotic systems is investigated. A novel Lyapunov sufficient condition for predefined time stability is presented, and an improved fractional order non-singular sliding mode surface is designed to weaken the restriction that the parameter

γ

must be positive odd. It is demonstrated that the degrees of freedom of the parameters associated with the sliding mode surface are increased. Then, an improved predefined time sliding mode controller is designed. This controller ensures the synchronization of the fractional order chaotic system within a predefined time interval by adjusting the predefined time

T_{p}

. An examination of the predefined time sliding mode synchronization control of fractional order Chua’s circuits is also conducted. Finally, the efficacy of the proposed controller is substantiated through numerical simulations, and a comparative analysis is conducted with existing predefined time controllers to assess its robustness and wide applicability.

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分数阶混沌系统的滑模控制时间同步

研究了分数阶Caputo混沌系统的预定义时间滑模控制。提出了一种新的Lyapunov时间稳定性的充分条件，并设计了一种改进的分数阶非奇异滑模曲面，以削弱参数γ必须为正奇数的限制。结果表明，与滑模面相关的参数的自由度增加了。然后，设计了一种改进的预定义时间滑模控制器。该控制器通过调节时间Tp来保证分数阶混沌系统在预定义的时间间隔内的同步。对分数阶蔡氏电路的时间滑模同步控制进行了研究。最后，通过数值仿真验证了所提控制器的有效性，并与现有的预定义时间控制器进行了对比分析，以评估其鲁棒性和广泛的适用性。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.