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COMPUTATION OF OPTIMAL CONTROL OF LINEAR SYSTEMS USING HAAR WAVELETS

A new method is presented for computation of optimal control for linear systems using Haar wavelets. The method is based on a novel operational matrix derived from integration of Haar wavelets. The optimal control problem is converted to a two-point-boundary-value problem, which is then solved using the Haar wavelet transformation. The proposed method is then extended to the numerical solution for optimization of singular systems. Accuracy of the solution can be improved by increasing the resolution of wavelet expansion, i.e., by increasing the order of transformation. Compared with known methods in the literature, the proposed method does not require explicit computation of wavelet coefficients, which makes it computationally more efficient and requires less computer memory. Simulation results are presented to illustrate the method.