Numerical solution of some initial optimal control problems using the reproducing kernel Hilbert space technique

In this paper, we present a general technique for solving a class of linear/nonlinear optimal control problems. In fact, an analytical solution of the state variable is represented in the form of a series in a reproducing kernel Hilbert space. Sometimes with the aid of this series form, we can also present the optimal control variable in a series form. An iterative method is given to obtain the approximate optimal control and state variables and the cost functional is numerically obtained. Convergence analysis of the method is also provided. Several numerical examples are tested to demonstrate the applicability and efficiency of the method.