Data-driven Methods for Control: from Linear to Lifting

The progress towards intelligent systems and digitalization relies heavily on the use of automation technology. However, the growing diversity of control objects presents significant challenges for traditional control approaches, as they are highly dependent on expert knowledge and require substantial commissioning effort. In response to this challenge, data-driven methods have emerged as a promising alternative that reduces human involvement by incorporating knowledge extracted from data. This thesis follows a conventional control research path and investigates the application of data-driven methods to linear time-invariant dynamics and nonlinear dynamics.

The first part of the thesis focuses on predictive control based on Willems' fundamental lemma. A tractable robust formulation based on the data-enabled predictive control (DeePC) framework is introduced, followed by a bi-level approach that aims to improve robustness and adaptivity. The focus then shifts to nonlinear dynamics, where reproducing kernel Hilbert space (RKHS) and Koopman operator-based heuristics are utilized to extend the applicability of Willems' fundamental lemma.

The second part of the thesis concentrates on stability analysis, which is a fundamental aspect of control science. Stability analysis must be robust enough to account for the infinitely many possible realizations of underlying dynamics based on a fixed finite set of data. To this end, a robust stability guarantee for a piece-wise affine (PWA) Lyapunov function is provided, which is a generalization of the classical Lyapunov-Massera local asymptotic stability theorem. Additionally, a convex second-order cone program (SOCP) is proposed to learn a robust PWA Lyapunov function assuming the underlying dynamics are Lipschitz. This approach provides a new means of designing stable control systems without requiring significant human intervention.

The last part of this thesis presents additional research on self-triggered control and real-time optimization algorithm design. These studies complement the primary investigation and provide a complete exposition of the research carried out during the Ph.D. program.