M03 - CANCELLED

In the realm of control engineering, we have traditionally focused on designing systems for stability and optimal performance, often relying on precise models of dynamic behavior. However, the increasing complexity and uncertainty inherent in modern cyber-physical systems demand a departure from purely model-centric approaches. This course is designed to equip you with the essential tools to navigate this evolving landscape. We will begin by exploring fundamental data-driven systems formalisms, laying the groundwork for how these concepts apply to data-driven control systems. The course will then delve into the practicalities of forecasting and classifying unknown system behaviors. A significant part of this section will also address uncertainty quantification, which is paramount for robust data- driven design. Moving beyond prediction, we will address the crucial aspect of probabilistic certification. This involves understanding sample complexity, exploring concepts of probabilistic scaling, and applying iterative methods and the theory of finite families to provide rigorous guarantees on system performance despite data-driven uncertainties. Finally, we will transition to optimization in data-driven systems. Here, we will investigate various first-order methods, delve into the intricacies of stochastic optimization, and examine the interplay between optimization and randomization in designing effective controllers. The course will conclude with a look at diverse Applications, including quartile regression, the generation of probabilistic invariant sets, and the implementation of stochastic model predictive control, demonstrating how these methodologies translate into practical solutions for complex control problems. 1. Introduction i. Data-driven systems formalisms a) Regression/classification b) Parametric/non-parametric ii. Deterministic vs randomized iii. Applications in data-driven control systems 2. Forecasting and classifying i. Kriging ii. Kernel methods iii. Uncertainty quantification 3. Probabilistic certification i. Sample complexity ii. Probabilistic scaling iii. Iterative methods and finite families 4. Optimization in data-driven systems i. First order methods ii. Stochastic optimization iii. Optimization and randomization 5. Applications i. Quartile regression ii. Probabilistic invariant sets iii. Stochastic model predictive control