A Parallel-in-Time Newton's Method for Nonlinear Model Predictive Control

TL;DR

This paper introduces a parallel-in-time Newton's method for nonlinear model predictive control, significantly reducing computation time by leveraging parallel algorithms and hardware, enabling faster control of complex systems.

Contribution

It develops a novel parallel-in-time second-order solver for constrained nonlinear optimization in MPC, utilizing associative operations and parallel scan algorithms for improved efficiency.

Findings

Achieves logarithmic computational time scaling over the planning horizon.

Demonstrates effectiveness on nonlinear, constrained dynamical systems.

Reduces computational burden for real-time MPC applications.

Abstract

Model predictive control (MPC) is a powerful framework for optimal control of dynamical systems. However, MPC solvers suffer from a high computational burden that restricts their application to systems with low sampling frequency. This issue is further amplified in nonlinear and constrained systems that require nesting MPC solvers within iterative procedures. In this paper, we address these issues by developing parallel-in-time algorithms for constrained nonlinear optimization problems that take advantage of massively parallel hardware to achieve logarithmic computational time scaling over the planning horizon. We develop time-parallel second-order solvers based on interior point methods and the alternating direction method of multipliers, leveraging fast convergence and lower computational cost per iteration. The parallelization is based on a reformulation of the subproblems in terms of associative operations that can be parallelized using the associative scan algorithm. We validate our approach on numerical examples of nonlinear and constrained dynamical systems.