Output Feedback Adaptive Control for Stochastic Non-strict-feedback System with Dead-zone

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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555

Output Feedback Adaptive Control for Stochastic Non-strict-feedback System with Dead-zone Yumei Sun*, Bingwei Mao, Hongxia Liu, and Shaowei Zhou Abstract: This paper focuses on the problem of adaptive neural network (NN) control for a class of nonlinear stochastic non-strict feedback system with dead-zone input. A novel adaptive NN output feedback control approach is first proposed for stochastic non-strict feedback nonlinear systems. In order to solve the problem of dead-zone input, a linear decomposition method is proposed. On the basis of the state observer, an output feedback adaptive NN controller is designed by backstepping approach. It is shown that the proposed controller guarantees that all the signals of the closed-loop systems are semi-globally uniformly bounded in probability. Simulation results further illustrate the effectiveness of the proposed approach. Keywords: Adaptive neural control, backstepping, dead-zone, state observer, stochastic non-strict feedback nonlinear systems.

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INTRODUCTION

Over the past decades, many scholars have dedicated much effort to handle the problems of the stability analysis and the control design for nonlinear systems. Applying the inherent approximation capability of fuzzy logical systems (FLSs) or neural networks(NNs), some fuzzy/neural controllers are employed in control design for nonlinear systems with unknown nonlinear functions. Wang et.al. [1] first proposed a stable adaptive fuzzy control scheme for a class of nonlinear systems with unknown functions. Since then based on the backstepping technique, some interesting results on nonlinear strict-feedback systems have been proposed [2–10] for deterministic systems via state feedback control strategy. Furthermore, adaptive fuzzy/neural control strategies were discussed for uncertain stochastic systems in [11–15]. In sense of finite-time stability, the problems of some nonlinear systems control have been studied in [16, 17]. While state variables are usually unknown or partly unknown in practice, the aforementioned control schemes by state feedback are hard to achieve. Therefore, some output-feedback control strategies were proposed in recent years, see [18–26]. With the help of the state observer, Chen et al. [18] addressed adaptive neural network control for class of non-strict feedback nonlinear system with input saturation. Tong et al. [19] addressed adaptive

NN backstepping control for a class of delayed large-scale systems, and decentralized adaptive NN output-feedback controllers were developed. Adaptive output feedback fuzzy/neural control strategies were developed under the sense of finite time stability in [22–24]. Notice that dead zone usually occurs in modern industrial field, such as pneumatic and hydraulic actuator, mechanical connection, electrical servomotor. Dead zone is one of the most important factors which affects system performance, reduces control precision and even leads to system instability. Thus, the control synthesis for non