Data-Driven Robust Predictive Control with Interval Matrix Uncertainty Propagation

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 shown to be recursively feasible and practically stable. A numerical example shows that the proposed approach compares favorably to existing methods based on zonotopic tubes and is competitive with an approach combining set-membership system identification and model-based predictive control.