Solving Optimal Control Problem for Linear Time Invariant Systems Via Chebyshev wavelet

Abstract

Over the last four decades, optimal control problem are solved using direct and indirect methods. Direct methods are casted in parameterization and discretization forms. Parameterizations are based on using polynomials to represent the optimal problem. The proposed direct method is based on transforming the optimal control problem into a mathematical programming problem. A wavelet-based method is used to parameterize the linear quadratic optimal control problem. The Chebyshev wavelets functions are used as the basis functions. Numerical examples are presented to show the effectiveness of the proposed method, and several optimal control problems were solved. The simulation results show that the proposed method gives good and comparable results.