Distributed Model Predictive Control for Piecewise Affine Systems Based on Switching ADMM

TL;DR

This paper introduces a distributed model predictive control method for piecewise affine systems that reduces computational complexity by solving convex problems using a novel ADMM-based approach, improving efficiency and performance.

Contribution

A new distributed MPC scheme for PWA systems utilizing an ADMM-based method to handle non-convexities, enabling convex optimization and better computational efficiency.

Findings

Significantly reduces CPU time compared to existing methods.

Improves closed-loop control performance.

Ensures stability and recursive feasibility under certain conditions.

Abstract

This paper presents a novel approach for distributed model predictive control (MPC) for piecewise affine (PWA) systems. Existing approaches rely on solving mixed-integer optimization problems, requiring significant computation power or time. We propose a distributed MPC scheme that requires solving only convex optimization problems. The key contribution is a novel method, based on the alternating direction method of multipliers, for solving the non-convex optimal control problem that arises due to the PWA dynamics. We present a distributed MPC scheme, leveraging this method, that explicitly accounts for the coupling between subsystems by reaching agreement on the values of coupled states. Stability and recursive feasibility are shown under additional assumptions on the underlying system. Two numerical examples are provided, in which the proposed controller is shown to significantly improve the CPU time and closed-loop performance over existing state-of-the-art approaches.