Structurally optimized wavelet network based adaptive control for a class of uncertain underactuated systems with actuator saturation

Abstract

In this paper, a structurally optimized wavelet network based adaptive control scheme is presented for a class uncertain underactuated system subjected to input constraints. This paper addresses the issue of curse of dimensionality associated with the multidimensional wavelet networks based on tensor product approach and presents a structural optimization scheme to tackle the problem of curse of dimensionality and to develop a parsimonious network structure. Optimization scheme utilizes genetic algorithm (GA) as the heuristic search technique to determine the optimal subset of the wavelet functions for the construction of wavelet network. Controller is developed by applying a two level hierarchical scheme and it incorporates wavelet network to mimic the system uncertainties as well as the nonlinear dynamics invoked by the actuator saturation. Boundedness of closed loop signals in uniform ultimate sense is proved by constructing a Lyapunov function. Results of the simulation demonstrate the effectiveness of proposed approach.