Optimal Control Problems: Convergence and Error Analysis in Reproducing Kernel Hilbert Spaces

In this article, we offer an efficient method to find an approximate solution for quadratic optimal control problems. The approximate solution is offered in a finite series form in reproducing kernel space. The convergence of proposed method is analyzed under some hypotheses which provide the theoretical basis of the proposed method for solving quadratic optimal control problems. Furthermore, in this study, we investigate the application of the proposed method to obtain the solution of equations that have formally been solved using Pontryagin’s maximum principle. Moreover, many different types of quadratic optimal control problems are considered prototype examples. The obtained results demonstrate that the proposed method is truly effective and convenient to obtain the analytic and approximate solutions of quadratic optimal control problems.