Robust Data-Driven Predictive Control using Reachability Analysis

TL;DR

This paper introduces a robust data-driven predictive control method that uses reachability analysis based on noisy input-output data, ensuring safety and performance without relying on a known system model.

Contribution

It develops a novel data-driven reachable region computation using matrix zonotope recursion, enabling robust control with bounded noise without statistical noise assumptions.

Findings

Achieves equivalent behavior to model predictive control in noise-free scenarios

Guarantees robust constraint satisfaction under bounded noise

Demonstrates effectiveness through numerical experiments

Abstract

We present a robust data-driven control scheme for an unknown linear system model with bounded process and measurement noise. Instead of depending on a system model in traditional predictive control, a controller utilizing data-driven reachable regions is proposed. The data-driven reachable regions are based on a matrix zonotope recursion and are computed based on only noisy input-output data of a trajectory of the system. We assume that measurement and process noise are contained in bounded sets. While we assume knowledge of these bounds, no knowledge about the statistical properties of the noise is assumed. In the noise-free case, we prove that the presented purely data-driven control scheme results in an equivalent closed-loop behavior to a nominal model predictive control scheme. In the case of measurement and process noise, our proposed scheme guarantees robust constraint satisfaction, which is essential in safety-critical applications. Numerical experiments show the effectiveness of the proposed data-driven controller in comparison to model-based control schemes.