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Wavelet based approximation in the optimal control of distributed parameter systems

Wavelet based Galerkin approximation schemes for the closed-loop solution of optimal linear-quadratic regulator problems for distributed parameter systems are developed. The methods are based upon the finite dimensional approximation of the associated operator algebraic Riccati equation in Galerkin sub-spaces spanned by families of compactly supported wavelet functions. An overview of the aspects of the theory of wavelet transforms which are useful in the development of Galerkin schemes has been provided. A brief outline of optimal linear-quadratic control theory for infinite dimensional systems together with the associated approximation and convergence theories have also been included. The results of numerical studies involving two examples, control of a one dimensional heat/diffusion equation and vibration damping in a visco-thermoelastic rod, are presented and discussed. Comparisons with existing methods using both spline and modal functions are made.