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The principal focus of our research is a new systematic approach to design optimal control algorithms that may be implemented on parallel machines. This approach is based on a two-level parametrization of first-order optimality conditions. The first level of parametrization is concerned with the decrease of the overall amount of operations, and the second level is concerned with parallelism. By introducing parametrization matrices in the first level and then factoring those matrices to exhibit the amount of parallelism desired in the second level as a function of the number of processing elements to be used, the resulting optimality conditions may be tailored to the computing network on which the computations are to be performed. Algorithm, Parallelism, Optimal control, Computer systems, Fault tolerant. (jes)