Solving Quadratic Optimal Control Problems using Legendre Function

Abstract

The proposed methods to solve optimal control problems are classified as direct methods and indirect methods. This thesis is based on solving optimal control problems using direct methods in which an optimal control problem is converted into a mathematical programming problem. The direct methods can be employed by using the parameterization technique which can be applied in three different ways: control parameterization, control-state parameterization and state parameterization. Here, we used control-state parameterization. This thesis presents numerical methods to solve unconstrained optimal control problems. The solution method is based on using the iteration approach to replace the nonlinear optimal control problem by a sequence of time-varying linear quadratic optimal control problems. Each of these problems is solved by converting it into quadratic programming problem. The control-state parameterization technique is done by using the Legendre polynomials to approximate the system state variables. The proposed method has been applied on several examples and we find that it gives acceptable results compared with some other methods.