Implementation of model predictive control for tracking in embedded systems using a sparse extended ADMM algorithm

TL;DR

This paper introduces a sparse, low-memory optimization algorithm based on an extended ADMM method for implementing model predictive control in embedded systems, enhancing robustness and feasibility.

Contribution

It presents a novel sparse optimization algorithm tailored for MPC tracking in embedded systems, exploiting problem structure for improved efficiency.

Findings

The proposed solver outperforms existing methods in simulation tests.

The algorithm maintains recursive feasibility despite reference changes.

It enables low-memory implementation suitable for embedded systems.

Abstract

This article presents a sparse, low-memory footprint optimization algorithm for the implementation of the model predictive control (MPC) for tracking formulation in embedded systems. This MPC formulation has several advantages over standard MPC formulations, such as an increased domain of attraction and guaranteed recursive feasibility even in the event of a sudden reference change. However, this comes at the expense of the addition of a small amount of decision variables to the MPC's optimization problem that complicates the structure of its matrices. We propose a sparse optimization algorithm, based on an extension of the alternating direction method of multipliers, that exploits the structure of this particular MPC formulation. We describe the controller formulation and detail how its structure is exploited by means of the aforementioned optimization algorithm. We show closed-loop simulations comparing the proposed solver against other solvers and approaches from the literature.