A collocation method for solving non-linear optimal control problems

In this paper we propose a new numerical method for solving optimal control problems. The state and control are approximated by their interpolants using Chebyshev nodes. The dynamics of the optimal control problem are collocated at the Chebyshev nodes and consequently are reduced to a system of algebraic equations. Instead of using cell averages to approximate the performance index our method uses Clenshaw quadrature whose weights are explicitly known. The complete problem now is solved by applying nonlinear programming technique. Some examples are included to show that the method is very efficient and easy to code.