On a constructive adaptive wavelet control approach

Abstract

Adaptive control approaches can successfully handle system parametric uncertainties, but can hardly deal with unstructured uncertainties. In adaptive neural network and adaptive fuzzy network approaches, the unstructured uncertainties are converted into parametric ones using artificially selected neural or fuzzy basis functions. In this paper we introduce adaptive wavelet network working concurrently with a traditional adaptive mechanism to handle both parametric and unstructured uncertainties. By virtue of the orthonormal and multi-resolution properties, the structure and coefficients of a wavelet network used to approximate an unstructured uncertainty not only exist but unique. Therefore the wavelet network structure can be made to evolve dynamically (constructively) from coarse to finer ones to achieve better approximation and meanwhile the adaptation results remain valid and consistent.