Online Control with Adversarial Disturbance for Continuous-time Linear Systems

We study online control for continuous-time linear systems with finite sampling rates, where the objective is to design an online procedure that learns under non-stochastic noise and performs comparably to a fixed optimal linear controller. We present a novel two-level online algorithm, by integrating a higher-level learning strategy and a lower-level feedback control strategy. This method offers a practical and robust solution for online control, which achieves sublinear regret. Our work provides one of the first nonasymptotic results for controlling continuous-time linear systems a with finite number of interactions with the system.