Parallel initial costate search algorithms for computing optimal controls

This paper describes a collection of parallel initial costate search algorithms suitable for implementation on an advanced computer with the facility for large scale parallel processing. Specifically, a parallel nongradient algorithm and a parallel variable metric algorithm have been used to search for the initial costate vector that defines the solution to the optimal control problem. To avoid the computational problems sometimes associated with simultaneous forward integration of both the state and costate equations, a parallel shooting procedure based upon partitioning of the integration interval was considered. Application of this parallel procedure to a forced Van der Pol system indicates that convergence time is significantly less than that required by highly efficient serial procedures.