Direct Adaptive Fuzzy Tracking Control of Non-affine Stochastic Nonlinear Time-Delay Systems
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Direct Adaptive Fuzzy Tracking Control of Non-affine Stochastic Nonlinear Time-Delay Systems Huanqing Wang1 • Licheng Shan1 • Xudong Zhao2 • Tieshan Li3
Received: 29 March 2020 / Revised: 31 May 2020 / Accepted: 13 July 2020 Ó Taiwan Fuzzy Systems Association 2020
Abstract In this research, the problem of direct adaptive fuzzy control based on state feedback for a class of nonaffine stochastic nonlinear systems with time delay is considered. Fuzzy logic systems (FLSs) and mean value theorem are utilized to overcome the design difficulties appeared in the unknown nonlinearities and non-affine structure, respectively. With the utilization of adaptive control and backstepping design framework, a direct adaptive fuzzy control method is developed. Through Lyapunov analysis, the presented controller can guarantee that the variables in the closed-loop system are all bounded in the fourth-moment, in the mean time, the output signal can track the given reference signal by appropriately selecting the design parameters. Simulation results are provided to illustrate the correctness of the theoretical results. Keywords Adaptive fuzzy control Time-delay systems Stochastic systems
& Huanqing Wang [email protected] Xudong Zhao [email protected] Tieshan Li [email protected] 1
Department of Mathematics, Bohai University, Jinzhou, Liaoning, People’s Republic of China
2
Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, China
3
College of Navigation, Dalian Maritime University, Dalian 116026, China
1 Introduction As it is well known, stochastic disturbance is widespread in practical systems such as manufacturing processes, robot operating systems, and power systems. The existence of stochastic disturbance may severely deteriorate the performance of control system and even result in instability. Then, the research on stochastic nonlinear systems is an interesting and challenge topic, and has attracted more and more scholars’ attention. Ever since the emergence of backstepping design method for stochastic nonlinear systems with strict-feedback form in [1], many researchers have extended the method to different kinds of stochastic systems for dealing with the various control problems [2–7]. For example, for the control problem of interconnected stochastic systems, a decentralized adaptive stabilization control scheme is proposed in [5]. Further, in [7], Psillakis handled the controller design for nonlinear systems with unknown covariance noise based on adaptive neural control approach [8, 9]. Thereafter, abundant results [10–22] on intelligent control for stochastic systems were achieved, but little progress was made in the plants with non-affine structure. In practical applications, there are many non-affine nonlinear systems, such as dynamic model of pendulum system, biochemical process, etc. The result on non-affine stochastic systems was first presented in [23] by using fuzzy adaptive control approach [24, 25]. Then, a large number of follow-up researches were reported fo
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