Legendre Coefficients Method for Linear-Quadratic Optimal Control Problems by Using Genetic Algorithms

In this paper, a numerical method for solving Linear-quadratic optimal control problems (LQPs) is presented. A method is provided for approximating the system dynamics, boundary conditions, and the performance index. The control and state variables are approximated by Legendre orthogonal polynomials. The method is based on using orthogonality of Legendre polynomials to get rid of the integration of the performance index. The problem is then reduced to a constrained optimization problem which is solved by Genetic Algorithms (GAs). Numerical results and comparisons are given at the end of this paper.