Journal of the
Korean Mathematical Society JKMS

This paper attempts to present a numerical method for solving optimal control problems. The method is based upon constructing the $n$-th degree Jacobi polynomials to approximate the control vector and use differentiation matrix to approximate derivative term in the state system. The system dynamics are then converted into system of algebraic equations and hence the optimal control problem is reduced to constrained optimization problem. Numerical examples illustrate the robustness, accuracy and efficiency of the proposed method.

Keywords: Jacobi polynomials, differentiation and integration matrices, optimal control problem

MSC numbers: Primary 65N35, 65L05, 65J10, 49J15