Robust Data-Driven Tube-Based Zonotopic Predictive Control with Closed-Loop Guarantees

TL;DR

This paper introduces a robust data-driven tube-based zonotopic predictive control method for discrete-time linear systems that guarantees stability and feasibility despite noise, using a two-phase approach involving model over-approximation and optimization.

Contribution

It presents a novel two-phase data-driven control framework that ensures recursive feasibility and robust stability for noisy linear systems using zonotope-based model approximation.

Findings

Guarantees robust exponential stability of the closed-loop system.

Ensures recursive feasibility through an optimization-based control formulation.

Demonstrates competitive performance in numerical simulations.

Abstract

This work proposes a robust data-driven tube-based zonotopic predictive control (TZPC) approach for discrete-time linear systems, designed to ensure stability and recursive feasibility in the presence of bounded noise. The proposed approach consists of two phases. In an initial learning phase, we provide an over-approximation of all models consistent with past input and noisy state data using zonotope properties. Subsequently, in a control phase, we formulate an optimization problem, which by integrating terminal ingredients is proven to be recursively feasible. Moreover, we prove that implementing this data-driven predictive control approach guarantees robust exponential stability of the closed-loop system. The effectiveness and competitive performance of the proposed control strategy, compared to recent data-driven predictive control methods, are illustrated through numerical simulations.