Parallel collocation solution of constrained optimal control problems

This paper presents a parallel collocation algorithm for the solution of a two-point boundary value problem (BVP) that involves index-1 differential-algebraic equations (DAEs) and inequality constraints due to complementarity conditions. BVP-DAEs of this type arise from the indirect approach to the solution of optimal control problems that control variable inequality constraints. In the collocation method presented here the differential and algebraic variables of the BVP-DAEs are approximated using piecewise polynomials on a mesh that may be nonuniform. A Newton interior point method is used to solve the collocation equations, and maintain feasibility of the inequality constraints. The implementation of the algorithm involves parallel evaluation of the collocation equations, parallel evaluation of the system Jacobian, and parallel solution of a boarded almost block diagonal (BABD) system to obtain the Newton search direction. A numerical example shows that the parallel implementation provides significant speedup when compared to a sequential version of the algorithm, and when compared to a direct method.