Intelligent controller design with UUB stability using Gaussian wavelet neural networks

Abstract

Purpose

A chaotic system is a nonlinear deterministic system that displays complex, noisy‐like and unpredictable behavior. The interest in chaotic systems lies mostly upon their complex, unpredictable behavior, and extreme sensitivity to initial conditions as well as parameter variations. Based on wavelet neural network's (WNN) online approximation ability, the purpose of this paper is to propose an adaptive Gaussian wavelet neural control (AGWNC) system to control a chaotic system.

Design/methodology/approach

The proposed AGWNC system is composed of a wavelet neural controller and a compensation tangent controller. The wavelet neural controller utilizes a Gaussian WNN to mimic an ideal controller, and the compensation tangent controller is designed to compensate the approximation error between the ideal and the wavelet neural controllers. The controller parameters of the proposed AGWNC can online tune in the Lyapunov sense, thus the uniformly ultimately bounded stability of closed‐loop system can be guaranteed.

Findings

The proposed AGWNC system is applied to a chaotic system. Simulation results are used to demonstrate the effectiveness and performance of the proposed AGWNC scheme. Simulation results show that not only the favorable control performance can be achieved but also the control efforts without any chattering phenomena. Moreover, all controller parameters can be online tuning by the derived adaptive laws based on the Lyapunov function.

Originality/value

The proposed AGWNC approach is interesting for the design of an intelligent control scheme. The main contributions of this paper are: the overall closed‐loop control system is globally stable in uniform ultimate boundedness; the tracking error can be asymptotically attenuated to a desired small level around zero by appropriate chosen parameters and learning rates; and the AGWNC system can achieve favorable tracking performance.

Citation

Hsu, C., Hsu, C., Lin, C. and Lee, T. (2009), "Intelligent controller design with UUB stability using Gaussian wavelet neural networks", International Journal of Intelligent Computing and Cybernetics, Vol. 2 No. 1, pp. 102-119. https://doi.org/10.1108/17563780910939264