Data-Driven Constrained Control

Ensuring safety is a fundamental challenge. Traditional methods often rely on precise mathematical models, which are difficult, impractical, or costly to obtain for real-world systems with complex, nonlinear dynamics. This dissertation develops direct data-driven control approaches that enable safe and efficient operation of nonlinear systems without requiring explicit models or performing system identification. This effort leverages machine learning, optimization, and control theory to bridge theoretical rigor and practical applicability. Deterministic guarantees are provided based on the Lipschitz continuity of the system, and probabilistic guarantees through scenario optimization. The computation of safe sets is performed using one-shot approaches with broad neural networks, as well as iterative algorithms based on active learning. Additionally, safe sampling is investigated to ensure safety in the data collection phase. Numerical experiments are performed on autonomous vehicles, chaotic Julia and Lorenz systems with fractal dynamics, and the Van der Pol oscillator.