Data-Driven Online Optimization and Control with Performance Guarantees

This thesis considers the analysis and design of algorithms for the management and control of uncertain intelligent systems which are observable through (limited) online-accessible data. Examples include online equity trading systems under extreme price fluctuations, robotic systems moving in unknown environments, and transportation systems subject to uncertain drivers’ actions and other (accident) events.To ensure safe, reliable, and resilient system behaviors, this thesis studies various theoretical problem scenarios, which focus on reducing uncertainty with performance guarantees via the assimilation of streaming data, the data-driven design of control, and online learning of system models, resilient operations in uncertain environments, and anomaly detection.These formulations are largely rooted in two mechanisms: online optimization and distributionally robust optimization, where the first enables online-tractable formulations of the problem, and the latter accounts for systemic uncertainty with high confidence. Both approaches are applicable beyond the particular systems of study, to virtually any type of dynamic system where sensitive data is progressively available and may be exploited to the advantage of management and control. This work is unique in that it brings together current tools in optimization, control of dynamical systems, data-based modeling and probability theory, significantly advancing the state of the art