Stability and robustness in data-driven predictive control

This thesis addresses data-driven model predictive control (MPC) with theoretical guarantees on closed-loop stability and robustness. The proposed approach relies on Willems' Fundamental Lemma which parametrizes all trajectories of an unknown linear system based on one measured trajectory. This result allows to design MPC schemes simply from data of the system rather than from its model, which need not be known. However, when applying such a scheme in closed loop, stability is not necessarily guaranteed.

To close this gap, we develop a framework for designing and analyzing MPC schemes, which are only based on input-output data and come with desirable closed-loop guarantees. We address various control objectives, including setpoint stabilization, tracking, and constraint satisfaction for linear or nonlinear systems and from noise-free or noisy data.

We demonstrate with numerical and experimental applications that the proposed framework not only contributes to a rigorous data-driven control theory, but is also simple to apply and provides high performance for challenging nonlinear control problems.