Numerical solution of a class of two-dimensional quadratic optimal control problems by using Ritz method

In this paper, we focus on a class of a two‐dimensional optimal control problem with quadratic performance index (cost function). We are going to solve the problem via the Ritz method. The method is based upon the Legendre polynomial basis. The key point of the Ritz method is that it provides greater flexibility in the initial and non‐local boundary conditions. By using this method, the given two‐dimensional continuous‐time quadratic optimal control problem is reduced to the problem of solving a system of algebraic equations. We extensively discuss the convergence of the method and finally present our numerical findings and demonstrate the efficiency and applicability of the numerical scheme by considering three examples. Copyright 2015 John Wiley & Sons, Ltd.