Tube-Based Robust Data-Driven Predictive Control

TL;DR

This paper introduces a robust data-driven predictive control method for unknown LTI systems using a single noisy trajectory, ensuring stability and constraint satisfaction through a tube-based approach.

Contribution

It develops a tractable, convex quadratic program-based control scheme that guarantees robustness and stability with minimal data requirements.

Findings

Controller guarantees recursive feasibility and constraint satisfaction.

Method demonstrates robustness and effective closed-loop performance in numerical examples.

Explicit bounds on prediction mismatch are derived from measurement noise.

Abstract

This paper presents a tractable tube-based robust data-driven predictive control scheme that uses only a single finite noisy input-state trajectory of an unknown discrete-time linear time-invariant (LTI) system. A simplex constraint is imposed on the Hankel coefficient vector, yielding explicit polyhedral bounds on the prediction mismatch induced by bounded measurement noise. Using certified initial and terminal robust positively invariant (RPI) sets, we derive a tube-tightened formulation whose online optimization problem is a strictly convex quadratic program (QP). The resulting controller guarantees recursive feasibility, robust satisfaction of input and state constraints, and practical input-to-state stability of the closed loop with respect to measurement noise. Numerical examples illustrate the effectiveness, robustness, and closed-loop performance of the proposed method.