Temporal Parallelisation of Dynamic Programming and Linear Quadratic Control

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