Decomposition and coordination for non-convex optimal control problems with parallel algorithm

A parallel algorithm is developed lor non-convex optimal control problems. The essential idea is to decompose the original problem into subproblems along the time axis so that subproblems can be solved in parallel. The decomposed problems has been proved to be equivalent to the original problem in the sense that there is an one-to-one correspondence between the local minima of the former with quadratic incentives and that of the latter under certain technical conditions. A parallel algorithm is developed to find the incentive coefficients and thus obtain the local minima of the original problem. The convergence properties are summarized and a simple numerical example is used to illustrate its feasibility.