Tube-Based Zonotopic Data-Driven Predictive Control

TL;DR

This paper introduces a new tube-based data-driven predictive control method for linear systems with bounded disturbances, using zonotopes derived from data to ensure stability and improve computational efficiency.

Contribution

It develops a novel approach that leverages reachability analysis and zonotopes from data to enhance predictive control of disturbed linear systems.

Findings

Effective control of a double-integrator with adversarial noise

Guarantees stability of the error zonotope

Improves computational efficiency of zonotopic MPC

Abstract

We present a novel tube-based data-driven predictive control method for linear systems affected by a bounded addictive disturbance. Our method leverages recent results in the reachability analysis of unknown linear systems to formulate and solve a robust tube-based predictive control problem. More precisely, our approach consists in deriving, from the collected data, a zonotope that includes the true state error set. We show how to guarantee the stability of the resulting error zonotope, which can be exploited to increase the computational efficiency of existing zonotopic data-driven MPC formulations. Results on a double-integrator affected by strong adversarial noise demonstrate the effectiveness of the proposed control approach.