A direct Approximation Method to solve OCP Using Laguerre Functions

Abstract

This paper presents an approximate method to solve unconstrained optimal control problem (OCP).This method is classified as a direct method in which an OCP is converted into a mathematical programming problem.The proposed direct method is employed by using the state parameterization technique with the aid of Laguerre polynomials and Laguerre functions to approximate the system state variables. To facilitate the computations within this method, new properties their proofs of Laguerre polynomials and Laguerre functions are given with proof.Furthermore, we will derive the condition under which the proposed method with Laguerre functions converges to the solution of the OCP equation. We will also show that for N (the number of basis functions) sufficiently large, the approximate states stabilize the system.The proposed method has been applied on several numerical examples and we find that it gives better or comparable results compared with some other methods.

Keywords

• a direct
• approximation
• method
• solve ocp using
• laguerre functions