A Hierarchical Decomposition for Large Scale Optimal Control Problems with Parallel Processing Capability

This paper presents a new method to decompose a large scale optimal control problem into a hierarchical optimization problem, in which low level subproblems have much shorter time horizon. The initial and final states of each subproblem are chosen as coordination parameters to glue all subproblems together. In such a decomposition, the high level problem is a parameter optimization problem, and subproblems are completely decoupled so that they can be solved in parallel. It is shown that the decomposed two-level optimization problem is equivalent to the original problem. Moreover, the high level problem is a convex parameter optimization problem if the original problem has a convex cost function and linear system dynamics. A parallel processing algorithm based on the gradient method for the high level problem is presented. A numerical example is used to illustrate the ideas and demonstrate the feasibility of the approach.