On the feasibility of finite differences homotopy-based algorithm for nonlinear optimal control problems

Abstract

Abstract In this paper, we examine the feasibility of continuation methods when used to solve the set of nonlinear equations obtained by discretizing finite horizon optimal control problems. We prove that, under some uniform boundness conditions on the optimal solutions, under classical convergence conditions on the discretization scheme and a boundness condition on the horizon length, there is a minimal number of grid points (depending on an a-priori specified maximal size of initial condition and horizon length) such that the resulting set of nonlinear equations can be imbedded in a homotopy that admits a feasible continuation algorithm.