Sliding mode control for a class of nonlinear systems based on robust adaptive neural network estimation

Abstract

Purpose

The purpose of this paper is to present a sliding mode controller design method for a class of uncertain nonlinear systems with uncertainties and to demonstrate a recursive derivative estimation procedure for the derivatives of system outputs.

Design/methodology/approach

A recursive derivative estimation procedure for the derivatives of system outputs is demonstrated. Radial basis function (RBF) neural networks are used to approximate the uncertainties and filters are introduced to estimate the derivatives of system outputs step‐by‐step. The adaptive tuning rules of RBF neural network weight matrices are derived by the Lyapunov stability theorem, which guarantees filter errors and network weight errors are bounded and exponentially converge to a neighborhood of the origin globally. The sliding mode controller is designed based on the estimation for the derivatives of system outputs such that the sliding surface converges to zero and the system control input is bounded.

Findings

The sliding mode controller can make the system output track the desired output with arbitrarily small tracking error. The filter errors and network weight estimation errors can be made arbitrarily small, and all the system signals are bounded. The proposed method does not need the supper bounds of the unmatched uncertainties and their any order derivatives.

Research limitations/implications

The system output and uncertainties are required to be sufficiently smooth in the proposed method. In practice, this condition is always satisfied generally.

Practical implications

This paper contains very useful advice for researchers on the sliding mode control and the use of neural networks.

Originality/value

The paper presents a new sliding mode controller design method based on recursive derivative estimation of system outputs using neural networks. The paper is aimed at theoretical researchers, especially those who have interest in sliding mode control, neural networks, adaptive techniques, and recursive estimation.

Citation

Deng, Y. and Zhang, Y. (2010), "Sliding mode control for a class of nonlinear systems based on robust adaptive neural network estimation", Kybernetes, Vol. 39 No. 6, pp. 888-899. https://doi.org/10.1108/03684921011046654