Finite-Time Adaptive Fuzzy DSC for Uncertain Switched Systems
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Finite-Time Adaptive Fuzzy DSC for Uncertain Switched Systems Qianjin Zhao1 • Xuemiao Chen1 • Jing Li2 • Jian Wu3
Received: 3 March 2020 / Revised: 10 April 2020 / Accepted: 13 May 2020 Taiwan Fuzzy Systems Association 2020
Abstract The finite-time adaptive fuzzy tracking control problem for a class of strict-feedback uncertain switched systems is investigated in this paper. Based on fuzzy approximation and adaptive dynamic surface control (DSC) technique, a finite-time adaptive state feedback fuzzy controller is developed via the common Lyapunov functions. Different from the existing works on uncertain switched systems, the DSC control scheme is developed based on a nonlinear filter to solve the ‘‘explosion of complexity’’ problem, and the structure of the proposed fuzzy controller is simple. Under the designed controller, all the signals of the closed-loop system remain semiglobally bounded, and within a finite-time interval, the system tracking error converges to an arbitrarily small region. That is, the semi-globally practical finite-time stability of the controlled system is guaranteed. To show the availability of the presented control scheme, a simulation example is given in this paper.
& Jian Wu [email protected] Qianjin Zhao [email protected] Xuemiao Chen [email protected] Jing Li [email protected] 1
College of Mathematics and Big Data, Anhui University of Science & Technology, Huainan, China
2
School of Mathematics and Statistics, Xidian University, Xi’an 710071, China
3
University Key Laboratory of Intelligent Perception and Computing of Anhui Province, Anqing Normal University, Anqing, China
Keywords Uncertain switched systems Fuzzy approximation Adaptive DSC technique Finite time stability
1 Introduction In the past decades, compared with asymptotic stabilization, the systems with finite-time convergence demonstrate some nice features, such as faster convergence, high accuracies and better robustness to uncertainties, and these benefits render that the method of finite-time stabilization becomes one of the most appealing tools in practical applications, lots of works have been obtained for a large variety of systems (e.g., see [1–11]). The fundamental research of the finite-time stability is proposed in [1]. Subsequently, a lot of finite-time control problems of linear/nonlinear systems have been solved. For the timevarying systems and impulsive dynamical systems, some sufficient conditions of the finite-time stability are established in [6, 7]. The finite-time control problems for timevarying linear systems are studied in [8, 9] using linear matrix inequalities (LMIs) method. For the disturbed system with mismatching condition, the problem of finite-time output regulation control is investigated based on a composite control design method in [10]. For a class of nonlinear time-varying interconnected systems, the decentralized control problem is studied in [12]. The finitetime stability problem of a class of homogeneous stochastic nonlinear systems modeled by stochastic differential equa
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