  This paper proposes a method for temporal parallelisation of dynamic
programming solutions of optimal control problems. We also derive the temporal
parallelisation of the linear quadratic tracking control problem. For these two
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. The computational benefits of the parallel methods
are demonstrated via numerical simulations run on a multi-core processor and a
graphics processing unit.
