A hybrid direction algorithm for solving optimal control problems

Abstract In this paper, we present an algorithm for finding an approximate numerical solution for linear optimal control problems. This algorithm is based on the hybrid direction algorithm developed by Bibi and Bentobache [A hybrid direction algorithm for solving linear programs, International Journal of Computer Mathematics, vol. 92, no.1, pp. 201–216, 2015]. We define an optimality estimate and give a necessary and sufficient condition to characterize the optimality of a certain admissible control of the discretized problem, then we give a numerical example to illustrate the proposed approach. Finally, we present some numerical results which show the convergence of the proposed algorithm to the optimal solution of the presented continuous optimal control problem.