Adaptive Fuzzy Dynamic Surface Control for Nonlinear Systems with Time-Varying Input Delay and Sampled Data
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Adaptive Fuzzy Dynamic Surface Control for Nonlinear Systems with Time-Varying Input Delay and Sampled Data XiaoDan Fan1 • KunTing Yu1
Received: 7 May 2020 / Revised: 12 June 2020 / Accepted: 13 July 2020 Ó Taiwan Fuzzy Systems Association 2020
Abstract This paper studies fuzzy adaptive dynamic surface control strategy for nonlinear system with sampled data and time-varying input delay. By utilizing the approximated property of fuzzy logic systems (FLSs), a fuzzy estimator (FE) model is designed to identify the states of the original system, which is mainly used to provide information of estimation states to replace the sampled data of the nonlinear controlled system. In the proposed strategy, with the help of sampled-data activity, an integral term is designed to compensate the problem of time-varying input delay. Moreover, by invoking the dynamic surface control (DSC) technique, the problem of ‘explosion of complexity’ has been overcame. And the developed control strategy demonstrates that all signals of the controlled system are semi-globally uniformly ultimately bounded (SGUUB). Ultimately, two numerical simulation examples are given to prove the feasibility of the developed control method and theory. Keywords Adaptive control Backstepping Timevarying input delay Dynamic surface control Sampleddata control
1 Introduction In recently years, since fuzzy logical systems (FLSs) can solve the uncertainties of the controlled systems with arbitrary modeling accuracy, the adaptive fuzzy control & KunTing Yu [email protected] 1
College of Science, Liaoning University of Technology, Jinzhou 121001, Liaoning, People’s Republic of China
strategy has been attracted a great attention and numerous theories and application results have been proposed in [1–6]. Recently, by combing FLSs and the backstepping technique, many fuzzy adaptive control strategies have been investigated for nonlinear systems in [7–11]. These methods do not need the controlled systems to satisfy the matching condition, or to satisfy the linear growth conditions. Thus, adaptive fuzzy backstepping control algorithm is one of the dominant methods of adaptive control. However, due to the process of recursive design, there is a disadvantage in backstepping control technique, which is ‘explosion of complexity’ problem. It should be noticed that the above-mentioned theories and application results all suffer it. To overcome this problem, DSC technique has been introduced and extensively used in [12–15]. In the working of [14], the one-order filter is introduced to filter virtual control signals, and virtual control signals are replaced by new states in recursive processes; hence, recursive differential of unknown nonlinear functions is solved and the problem of ‘‘explosion of complexity’’ is avoided. Based on this algorithm, and by combing the function separation technique and mean value theory, [15] has extended the DSC algorithm to pure-feedback systems with the unknown time-delay functions. Furthermore, in practical engineering application, dela
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