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