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This paper proposes a general formulation for temporal parallelisation ofdynamic programming for optimal control problems. We derive the elements andassociative operators to be able to use parallel scans to solve these problemswith logarithmic time complexity rather than linear time complexity. We applythis methodology to problems with finite state and control spaces, linearquadratic tracking control problems, and to a class of nonlinear controlproblems. The computational benefits of the parallel methods are demonstratedvia numerical simulations run on a graphics processing unit.

Temporal Parallelisation of Dynamic Programming and Linear Quadratic Control