Adaptive fixed-time control for Lorenz systems
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ORIGINAL PAPER
Adaptive fixed-time control for Lorenz systems Huanqing Wang · Hanxue Yue · Siwen Liu · Tieshan Li
Received: 14 May 2020 / Accepted: 27 October 2020 © Springer Nature B.V. 2020
Abstract This paper focuses on the problem of fixedtime chaos suppression and stabilization of a class of Lorenz systems with uncertain parameters. Based on the fixed-time stability theory, adaptive control and backstepping algorithm, a novel adaptive practical fixed-time controller is proposed. It is shown that the presented control scheme can guarantee that all the signals of the closed-loop system are bounded and chaotic phenomenon is suppressed in the fixed time. Both the theoretical analysis and simulation results verify the effectiveness of the proposed control strategy. Keywords Adaptive backstepping control · Fixedtime control · Lorenz system
H. Wang (B)· H. Yue · S. Liu College of Mathematical Sciences, Bohai University, Jinzhou 121000, Liaoning, People’s Republic of China e-mail: [email protected] H. Yue e-mail: [email protected] T. Li School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, People’s Republic of China T. Li School of Navigation College, Dalian Maritime University, Dalian 116026, People’s Republic of China e-mail: [email protected]
1 Introduction Chaos, an irregular and uncertain phenomenon of complex nonlinear dynamical systems, has been extensively investigated over the past decades. In the area of chaotic control, Lorenz system is often regarded as a typical exemplification, since it contains many characteristics of chaotic dynamics [1–3]. Hence, numerous remarkable methods and techniques have been proposed by some researchers to suppress the chaos phenomenon and stabilize the chaos systems, for instance, bang-bang control [4], adaptive control [5,6], impulsive control [7], and so on [8]. Among them, adaptive control, based on backstepping technique, is a main method for suppressing and stabilization of the chaotic systems [9,10]. Backstepping, a method based on recursion Lyapunov, was proposed in the early 1990s and has been comprehensively studied by Krstic, Kanellakopoulos and Kokotovic in [11]. It can avoid the cancellations of the useful nonlinearities and realize regulation and tracking performance. However, it is limited to dealing with the systems with known parameters. To solve the controller design problem for the nonlinear systems with uncertain parameters, adaptive backstepping control technology was developed in [11], which can realize the global stability and asymptotic tracking. Heretofore, there have been numerous remarkable achievements on adaptive backstepping control in the studies [12–17]. For example, Ahn and Nam et al. in [14] investigated the adaptive posi-
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tion control problem for the pump-controlled electrohydraulic actuator system. In [15], Zheng et al. presented a cloud-aided adaptive backstepping approach for nonlinear active full-vehicle suspension system. In [17], a backstepping-based adaptive cont
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