Wavelet Galerkin METHODES FOR GAME THEORETIC CONTROL OF DISTRIBUTED PARAMETER SYSTEMS

This paper presents a novel strategy for obtaining finite dimensional approximations of Riccati operators arising in game theoretic control problems on Hilbert spaces. While extensive progress has been made in the utilization of the newly developed field of wavelet analysis in signal and image processing, for less progress has been made in applicationa to computational mechanics. This fact is surprising considering the inherent multiresolution properties of wavelet analysis. This paper derives a wavelet galerkin formulation of a specific class of computational control problems: zero sum dynamic games on Hilbert spaces. This work extends previous research in that not only are convergence, exponential stability and robust stability of soft constrained differtial games on Hilbert spaces considered, but quantitative numerical conditioning results are also presented. In fact, a precise bound is given on the error induced by truncating wavelet quadratures used in the weak formulation of computational control problems. The theory presented is verified by modeling a robust control strategy for a beam subjected to piezocerarnic actuation and structured uncertainty.