Robust Data-driven Control with Safety Constraints and Fault Detection

Direct data-driven control has emerged as a powerful alternative to traditional state-space model-based methods by directly learning control policies from data. Nevertheless, ensuring that control actions adhere to specific physical and safety constraints, a challenge often overlooked in existing direct data-driven approaches focused primarily on stability and robustness, is crucial for real-world deployment. This paper addresses this gap by designing a robust data-driven state feedback control law that enforces safety-critical state constraints. Utilizing robust control techniques, we transform pointwise-in-time state constraints into reachable set constraints and formulate a semi-definite program (SDP) based on noisy input-state measurements. Additionally, recognizing that various system variations and environmental disturbances can be modeled as process noise, we propose to maximize the noise tolerance of the system through a data-driven SDP, thereby enhancing resilience against operational uncertainties. To further ensure operational safety, we develop a state estimator-based fault detector that leverages noisy closed-loop state data to trigger alarms during abnormal system operation. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed safe data-driven control approach.