Abstract
Differential Dynamic Programming (DDP) is an optimal control algorithm that has been used in a variety of applications involving optimization of dynamic systems. This paper discusses modifications in the serial DDP algorithm required to develop an efficient parallel algorithm. The modifications change the order of calculations in order to minimize the number of required barrier synchronization points within a time step. Because DDP is a fine-to-medium grained algorithm, previous approaches to parallel processing of DDP and related algorithms have focused on parallel processing across time steps, which results in a substantial loss of efficiency. The approach described here is most efficient for problems with a high state variable dimension. Numerical results indicate that for problems with 1000 state variables, our method can obtain a speedup of 5.3 on six processors (95.6% of the Amdahl upper bound), which is substantially higher than published results from earlier studies investigating problems of smaller state dimension and larger time dimension.
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