Feedback Control of Data-Driven Control Systems with Time Delays

This project advances mathematical control theory by developing data-driven feedback control methods to ensure desirable behavior in dynamical systems -- models commonly found in engineering and applied sciences. The research addresses challenges posed by partial or time-delayed state information, focusing on mitigating uncertainty and delays that arise in real-world systems, especially in aerospace applications. Theoretical developments will be validated through numerical simulations and applied to aircraft model scenarios where time delays and communication lags can lead to instability. The methods aim to provide performance guarantees, such as accurate path tracking and obstacle avoidance, to improve the safety of aerial systems used in defense, search and rescue, and space exploration. The project also trains PhD students in interdisciplinary research and promotes broader engagement between mathematics and engineering through publications and presentations. The project tackles key mathematical challenges in achieving feedback control goals for data-driven systems with delays, using three integrated strategies. The first uses an emulation approach to provide novel bounds on allowable input or measurement delays under which existing data-driven methods -- such as concurrent learning -- remain effective. This includes error analysis to test the investigator's conjecture that less frequent sampled output measurements from data-driven systems produce reduced tolerance to delays and derives new conditions under which control goals are still achieved despite delay uncertainty. The second strategy develops delay compensation methods to reduce the limitations imposed by delays in emulation-based approaches. These methods may include uncertain delays, variants of exact predictor approaches applied to liftings of the systems, and chain predictors in which longer input delays, or less frequently available measurements from systems can call for higher dimensional dynamical extensions that contain more predictors. The third strategy focuses on state-constrained systems, using tools such as barrier Lyapunov functions, reference governors, and robust forward invariance to derive tight bounds on allowable uncertainties while ensuring that control goals -- potentially with finite time deadlines -- are still met. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.