# Temporal Parallelisation of Dynamic Programming and Linear Quadratic Control

arXiv: https://arxiv.org/abs/2104.03186 · HTML: https://mlsanity.com/paper/2104.03186/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Apr 2021.

## Built on by (most cited first, 1 of 1)

- [Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPU](https://mlsanity.com/paper/2604.07644/) (2026)

## Abstract (arXiv)

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.