Data-driven distributed MPC of dynamically coupled linear systems

TL;DR

This paper introduces a novel data-driven distributed MPC method for stabilizing interconnected linear systems using only input-output data, ensuring recursive feasibility and stability without explicit models.

Contribution

It develops a distributed MPC scheme based on Willems' Fundamental Lemma, enabling trajectory parametrization solely from data and guaranteeing stability and feasibility.

Findings

Successfully stabilizes coupled linear systems

Ensures recursive feasibility of the control scheme

Demonstrates effectiveness through numerical example

Abstract

In this paper, we present a data-driven distributed model predictive control (MPC) scheme to stabilise the origin of dynamically coupled discrete-time linear systems subject to decoupled input constraints. The local optimisation problems solved by the subsystems rely on a distributed adaptation of the Fundamental Lemma by Willems et al., allowing to parametrise system trajectories using only measured input-output data without explicit model knowledge. For the local predictions, the subsystems rely on communicated assumed trajectories of neighbours. Each subsystem guarantees a small deviation from these trajectories via a consistency constraint. We provide a theoretical analysis of the resulting non-iterative distributed MPC scheme, including proofs of recursive feasibility and (practical) stability. Finally, the approach is successfully applied to a numerical example.