Laguerre Polynomials and Gradient Descent Approach for Linear Quadratic Optimal Control

Abstract

This paper presents a computational approach for solving linear time invariant quadratic optimal control system problem. The proposed approach is classified as a direct method, which is utilized by applying state and control parametrization using a finite length of Laguerre polynomials as a basis function with unknown parameters. In addition, the stochastic gradient descent approach was used to estimate the optimal parameters. Furthermore, this paper provides numerical examples to demonstrate the proficiency of the proposed method. The results of this study showed that using the direct method along with the stochastic gradient descent techniques were effective in solving the linear time invariant quadratic optimal control system problem.