Large-scale convex optimal control problems: time decomposition, incentive coordination, and parallel algorithm

A parallel algorithm based on time decomposition and incentive coordination is developed for long-horizon optimal control problems. This is done by first decomposing the original problem into subproblems with shorter time horizon, and then using the incentive coordination scheme to coordinate the interaction of subproblems. For strictly convex problems it is proved that the decomposed problem with linear incentive coordination is equivalent to the original problem, in the sense that each optimal solution of the decomposed problem produces one global optimal solution of the original problem and vice versa. In other words, linear incentive terms are sufficient in this case and impose no additional computation burden on the subproblems. The high-level parameter optimization problem is shown to be nonconvex, despite the uniqueness of the optimal solution and the convexity of the original problem. Nevertheless, the high-level problem has no local minimum, even though it is nonconvex. A parallel algorithm based on a prediction method is developed, and a numerical example is used to demonstrate the feasibility of the approach