ADMM for Exploiting Structure in MPC Problems

TL;DR

This paper presents a novel ADMM-based approach for model predictive control that exploits system structure through decomposition, leading to improved scalability, parallelization, and performance in complex control problems.

Contribution

It introduces a new structure-exploiting ADMM method with subsystem-specific penalties and a measure of system separation, enhancing efficiency and adaptability in MPC.

Findings

Favorable computational scaling with problem size

High degree of parallelizability

Improved performance over conventional ADMM

Abstract

We consider a model predictive control (MPC) setting, where we use the alternating direction method of multipliers (ADMM) to exploit problem structure. We take advantage of interacting components in the controlled system by decomposing its dynamics with virtual subsystems and virtual inputs. We introduce subsystem-individual penalty parameters together with optimal selection techniques. Further, we propose a novel measure of system structure, which we call separation tendency. For a sufficiently structured system, the resulting structure-exploiting method has the following characteristics: (i) its computational complexity scales favorably with the problem size; (ii) it is highly parallelizable; (iii) it is highly adaptable to the problem at hand; and (iv), even for a single-thread implementation, it improves the overall performance. We show a simulation study for cascade systems and compare the new method to conventional ADMM.