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Adaptive Fuzzy Dynamic Surface Control of Nonlinear Constrained Systems With Unknown Virtual Control Coefficients


Abstract:

This paper studies the problem of adaptive fuzzy dynamic surface control (DSC) of nonstrict-feedback nonlinear systems subject to unknown virtual control coefficients, de...Show More

Abstract:

This paper studies the problem of adaptive fuzzy dynamic surface control (DSC) of nonstrict-feedback nonlinear systems subject to unknown virtual control coefficients, dead zone, and full state constraints. The Nussbaum gain technique is used to overcome the difficulty caused by the unknown virtual control coefficients. By utilizing the information of tan-type barrier Lyapunov function, the requirement of full state constraints is successfully achieved. In addition, to handle the problem of “explosion of complexity” resulted from backstepping itself, a DSC approach using the sliding mode differentiator is introduced. Then, based on backstepping control, we develop a new adaptive fuzzy DSC strategy, which ensures that all state constrains are not violated via designing parameters appropriately. Meanwhile, other signals existing in the closed-loop system are bounded. Finally, comparative results are provided to illustrate the effectiveness of the proposed approach.
Published in: IEEE Transactions on Fuzzy Systems ( Volume: 28, Issue: 8, August 2020)
Page(s): 1737 - 1747
Date of Publication: 05 June 2019

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I. Introduction

Lower triangular nonlinear systems are a special class of nonlinear systems, which can be used to describe a large number of practical systems such as Brusselator model, one-link robot system, ball, and beam system, etc., and the research of such systems has drawn intensive attention in recent years. Some excellent control schemes [1]–[9] have been reported. In particular, adaptive fuzzy/neural control is one of the effective control schemes, which has been widely studied since fuzzy logic system (FLS) and neural network have a good theoretical property in approximating the unknown nonlinear function (see [10]–[13] and the references therein). However, the control schemes mentioned above cannot be directly applied to nonlower triangular nonlinear systems such as pure-feedback system and nonstrict-feedback system [14]–[19] . For nonstrict-feedback system, the nonlinear function existed in the th subsystem involves full state variables , which may result in algebraic loop problem if those methods of lower triangular system [2], [4], [20] are adopted directly. To tackle such a difficulty, much work has been reported. To list a few, in [21], the authors developed a suite of adaptive optimal control for a kind of nonlinear discrete-time system expressed in nonstrict-feedback form. In [22], based on backstepping technique, Chen et al. developed an effective approach called variable separation to overcome the difficulty resulted from the nonstrict-feedback structure. However, the result in [22] requires that the nonlinear functions are monotonically increasing. To relax such a restriction on nonlinear functions , Tong et al. in [23] proposed a new control scheme utilizing the property of fuzzy basis functions, which makes the controller design process simpler.

References

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