High-Confidence Data-Driven Safe Tracking Control Design

This article presents a high-confidence data-driven safe tracking control design for stochastic linear discrete-time systems. The high-confidence safe reference tracking for an ellipsoidal safe set is first formalized using the concept of probabilistic set-based $\lambda $ -contractivity. A data-driven controller, composed of feedback and feedforward elements, is then designed to enforce the $\lambda $ -contractivity of the safe set. The feedback control gain is learned by 1) providing a data-driven representation of the closed-loop system, which contains a decision variable that affects the control gain and 2) optimizing the decision variable to ensure the $\lambda $ -contractivity. This feedback term can be learned using a data set that is not even rich enough to identify the full system model. A feedforward gain learning algorithm and a data-driven reference governor are provided to satisfy the required conditions on equilibrium terms. It is shown that under certain conditions on the equilibrium terms, the learned tracking controller guarantees the system's safety and stability with high probability. The reference governor dynamically manipulates the desired reference signal based on the data quality to prevent any breach of safety constraints in a probabilistic manner. It is shown that the output of the reference governor eventually converges to the desired goal states if inside the safe set and high-quality data is available. Therefore, the tracking controller guarantees convergence of the system output to its desired goal while ensuring safety with a high probability. The simulation results on a drone hovering and a test system, comparing the results with the existing literature, confirm that the presented high-confidence data-driven safe tracking control outperforms certainty-equivalent safe control methods.