Numerical solution of optimal control problems

This paper introduces a numerical technique for solving optimal control problems which approximates both the state and control variables by Fourier series with unknown coefficients. An algorithm is provided for approximating the system dynamics, boundary conditions, and objective functional. Application of this method results in the transformation of differential and integral expressions into systems of algebraic expressions in the Fourier coefficients; the optimal control problems then become mathematical programming problems. Linear–quadratic problems can be transformed into unconstrained programming problems. Numerical examples are given to illustrate the simplicity and efficiency of this approach.