A Parallel Dual Fast Gradient Method for MPC Applications

TL;DR

This paper introduces a parallel dual fast gradient method for model predictive control that enhances computational efficiency and stability by solving subproblems in parallel with adaptive constraint tightening.

Contribution

It presents a novel parallel algorithm that splits the MPC problem into independent subproblems, computes tightening parameters adaptively, and ensures stability and feasibility.

Findings

Significant reduction in computation time compared to nonparallel methods.

Improved numerical conditioning and performance in simulations.

Effective handling of error propagation through adaptive tightening.

Abstract

We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying algorithm first splits the original problem in as many independent subproblems as the length of the prediction horizon. Then, our algorithm computes a solution for these subproblems in parallel by exploiting auxiliary tightened subproblems in order to certify the control law in terms of suboptimality and recursive feasibility, along with closed-loop stability of the controlled system. Compared to prior approaches based on constraint tightening, our algorithm computes the tightening parameter for each subproblem to handle the propagation of errors introduced by the parallelization of the original problem. Our simulations show the computational benefits of the parallelization with positive impacts on performance and numerical conditioning when compared with a recent nonparallel adaptive tightening scheme.