Solving Optimal Control Problem Via Chebyshev Wavelet

Abstract

Over the last four decades, optimal control problem are solved using direct and indirect methods. Direct methods are based on using polynomials to represent the optimal problem. Direct methods can be implemented using either discretization or parameterization. The proposed method in my thesis is considered as a direct method in which the optimal control problem is directly converted into a mathematical programming problem. A wavelet-based method is presented to solve the non-linear quadratic optimal control problem. The Chebyshev wavelets functions are used as the basis functions. The proposed method is also based on the iteration technique which replaces the nonlinear state equations by an equivalent sequence of linear time-varying state equations which is much easier to solve. Numerical examples are presented to show the effectiveness of the method, several optimal control problems were solved, and the simulation results show that the proposed method gives good and comparable results with some other methods.