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.