Adaptive supervisory WCMAC neural network controller (SWC) for nonlinear systems

Abstract

This paper proposes a wavelet-based cerebellar model arithmetic controller neural network (called WCMAC) and develops an adaptive supervisory WCMAC control (SWC) scheme for nonlinear uncertain systems. The WCMAC is modified from the traditional CMAC for obtaining high approximation accuracy and convergent rate using the advantages of wavelet functions and fuzzy TSK-model. For nonlinear uncertain systems, a PD-type WCMAC controller with filter is constructed to approximate an ideal control signal. The corresponding adaptive supervisory controller is used to recover the residual of approximation error. Finally, the adaptive SWC scheme is applied to chaotic system identification and control including Mackey-Glass timeseries prediction, control of inverted pendulum system, and control of Chua circuit system. These demonstrate the effectiveness of our adaptive SWC approach for nonlinear uncertain systems.

Experimental implementation of nonlinear TORA system and adaptive backstepping controller design

“…As in the above description, the WNN has adjustable parameters m, r, and w. Note that the used WNN is the same as our previous result in [17], the approximation property and ability has been demonstrated by illustration examples of nonlinear systems identification and control. More details can be found in literature [17]. In this study, the WNNs are adopted to estimate system uncertainties.…”

“…Several researchers have shown that a wavelet-based neural network achieves superior performance in network size and learning ability [7,17,25,27]. In this paper, to achieve closely approximated accuracy and speed up the convergence, wavelet-based functions are adopted to replace the membership functions of the fuzzy neural network (FNN) [5,14,15].…”

“…If system uncertainty and external disturbances exist, then the results may be unstable. Therefore, a neural network is used to approximate the unknown functions (or uncertainty) to solve this problem [5,8,9,14,17,18,27,28]. Herein, we propose a wavelet-based neural network (WNN) system to enhance the approximation of the unknown functions.…”

“…In our previous results, we developed fuzzy neural networks to approximate the unknown functions for nonlinear system identification and control [5,14,15]. Many researches have shown that using a wavelet basis can provide superior performance in network size and learning ability [7,11,17,19,20,25,27]. As a result, wavelet functions are combined with fuzzy neural networks to construct WNN systems.…”