Parallel Algorithms for Large Scale Optimal Control Programs

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Currently, there is no parallel algorithm that can solve optimal control problems efficiently on computers with a large number of processors. This research will develop two parallel algorithms to solve large scale optimal control problems that are expected to be efficient with a large number of processors. The first algorithm, called the Hybrid algorithm, is a combination of the Differential Dynamic Programming (DDP) and a stagewise Newton's method, both of which are serial. The Hybrid parallel algorithm is designed primarily for unconstrained optimal control problems. The second algorithm, called an SQP-type algorithm, is derived by utilizing special features of the optimal control problem along with a Sequential Quadratic Programming (SQP) approach. The SQP-type algorithm is suitable for both the unconstrained and constrained optimal control problem. In both algorithms, each processor is assigned to solve an optimization problem over a group of time periods. Codes will be developed for machines with medium-grain parallel capabilities e.g., the Intel iPSC/860 and Kendall Square computers. A typical engineering application involving a nonlinear flexible structural problem with 10,000 time periods will be used to evaluate the proposed algorithms.