Data-Driven Robust Predictive Control with Interval Matrix Uncertainty Propagation

TL;DR

This paper introduces a data-driven robust predictive control method for linear systems with unknown disturbances, using interval matrices and matrix zonotopes to ensure constraint satisfaction and stability.

Contribution

It develops a novel uncertainty propagation technique with interval matrices and matrix zonotopes for robust predictive control, improving over existing zonotopic methods.

Findings

Proves recursive feasibility and practical stability of the control scheme.

Demonstrates improved performance compared to existing zonotopic tube methods.

Validates effectiveness through a numerical example.

Abstract

This paper presents a new data-driven robust predictive control law, for linear systems affected by unknown-but-bounded process disturbances. A sequence of input-state data is used to construct a suitable uncertainty representation based on interval matrices. Then, the effect of uncertainty along the prediction horizon is bounded through an operator leveraging matrix zonotopes. This yields a tube that is exploited within a variable-horizon optimal control problem, to guarantee robust satisfaction of state and input constraints. The resulting data-driven predictive control scheme is proven to be recursively feasible and practically stable. A numerical example shows that the proposed approach compares favorably to existing methods based on zonotopic tubes.