Direct collocation and nonlinear programming for optimal control problem using an enhanced transcribing scheme

In this paper, an enhanced transcribing scheme is proposed for solving optimal control problems using direct collocation and nonlinear programming. This new scheme is based on the standard method of direct collocation that converts an optimal control problem into a nonlinear programming problem via simultaneous state and control discretization. When compared with the standard method, the enhanced scheme has the advantage of higher solution accuracy with minimal additional computational effort. It is particularly suited for systems with states that are related to each other in a special form. For such systems, the ensuing nonlinear programming problem has the same number of constraints as those using standard method. Numerical results on several optimal control problems using the enhanced scheme are presented, together with comparisons of the results obtained from standard scheme.