A hierarchical decomposition for large-scale optimal control problems with parallel processing structure

Abstract This paper presents a new method in solving long horizon optimal control problems. The original problem is decomposed along the time axis to form many smaller subproblems, and a high level problem is created that uses initial and terminal states of subproblems as coordination parameters. In such a scheme, the high level problem is a parameter optimization problem. Subproblems are optimal control problems having shorter time horizon, and are completely decoupled so that they can be solved in parallel. It is shown that the two-level problem has the same global optimum as the original one. Moreover, the high level problem is a convex programming problem if the original problem has a convex cost function and linear system dynamics. A parallel, two-level optimization algorithm is then presented, where the the high level problem is solved by Newton's method, and low level subproblems are solved by the Differential Dynamic Programming technique. Numerical testings on two examples are given to illustrate the idea, and to demonstrate the potential of the new method in solving long horizon problems under a parallel processing environment.

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