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In this paper, the Epsilon-Ritz method is used with piecewise constant orthogonal functions such as Walsh and Block-pulse to find solutions for the optimal feedback control and the system parameter identification problems. The two solutions are then combined to render an adaptive optimal control computational method. The computations utilized the VEC notations developed by Brewer  which is straight forward and convenient for implementation on parallel machines. Simulation results are shown indicating superiority of the proposed method.