A robust adaptive control method for Wiener nonlinear systems

Abstract

This paper proposes a new robust adaptive control method for Wiener nonlinear systems with uncertain parameters. The considered Wiener systems are different from the previous ones in the sense that we consider nonlinear block approximation error, process noise, and measurement noise. The parameterization model is obtained based on the inverse of the nonlinear function block. The adaptive control method is derived from a modified criterion function that can overcome non-minimum phase property of the linear subsystem. The parameter adaptation is performed by using a robust recursive least squares algorithm with a deadzone weighted factor. The control law compensates the model error by incorporating the unmodeled dynamics estimation. Theoretical analysis indicates that the closed-loop system stability can be guaranteed under mild conditions. Numerical examples including an industrial problem are studied to validate the results. Copyright In the literature, the control problem of Wiener systems has been mostly analyzed in model-based approaches [12][13][14][15][16][17]. In view of uncertainties, some other interesting approaches are also developed in an adaptive context. In a pioneering work [18], Pajunen introduced an inverse function to approximate the nonlinear block and derived a discrete-time nonlinear adaptive control. The main limitation of the result is that the inverse function is assumed to approximate the nonlinear block precisely; if not, there will be a residual tracking error. The subsequent paper [19] further achieves the stability results in the ordinary differential equation framework. Later, the aforementioned idea is also extended to Wiener systems described in a state-space form [20]. Recently, alternative choices are presented: Peng et al. [21] developed a neural network-based adaptive generalized predictive control; Pupeikis [22] proposed an efficient compensator for Wiener systems with saturation nonlinearities; Zhang and Mao [23] derived a locally stable adaptive control without the invertible nonlinear function assumption; and Silva et al. [24] introduced a successful practical application of Wiener model structure-based adaptive control.Despite the salient features of the aforementioned adaptive control methods, it still faces many important challenges: (i) the linear subsystem is assumed to be of minimum phase; (ii) nonlinear block approximation error is neglected; and (iii) the effect of stochastic disturbances is not fully addressed. To this end, the development of a general framework for adaptive control of Wiener nonlinear systems is still an open problem of major relevance, and it is also the motivation of this work.This paper focuses on the discrete-time robust adaptive control problem of Wiener nonlinear systems with uncertain parameters. The considered Wiener systems are more general and practical than the previous ones because non-minimum phase property of the linear subsystem, nonlinear block approximation error, process noise, and measurement noise are all considered. Based on t...

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“…It is well known that various practical systems frequently encounter nonlinearities to some extent. [1][2][3] In the past few years, much work has focused on developing modeling and identification of nonlinear dynamic systems. [4][5][6] Some practical nonlinear systems, such as industrial process, which can use their mechanism characteristics to model.…”

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