Optimal point-wise control of distributed parameter systems based on wavelet transform

Point-wise control is a typical control strategy for distributed parameter systems control. Since the employment of δ-function in point-wise control, it becomes very difficult to design the control law. The orthogonal function approximation is applied to deal with the optimal point-wise control of distributed parameter systems, and Haar wavelets have been chosen as orthogonal functions in this paper. The differential operational matrix and the product integrated operational matrix of Haar wavelet base have been proposed. The various operational matrices have been applied to convert the optimal point-wise control of distributed parameter systems to the lumped one, and an approximation algorithm has been obtained. The illustrated simulation results have validated the efficiency of the presented algorithm.