Prior-Informed Online Data-Driven Safe Control via LMI and Uncertainty-Set Update

Abstract

Model-prior-aided data-driven safe control methods often rely on batch datasets collected offline, which limits their ability to exploit information acquired during operation. This paper develops an online safe-control framework for discrete-time linear time-invariant systems with parametric uncertainty and bounded disturbances, where the uncertainty description is iteratively updated using newly acquired measurements. At each update, a data-consistency set is constructed from a sliding window of state-input samples and blended with a current prior model uncertainty set through a convex blending rule. We then solve a convex Linear Matrix Inequalities-based (LMI-based) synthesis problem that returns a robustly invariant ellipsoidal safe set and an associated state-feedback controller. The LMI certificate multipliers further define a normalized blending coefficient used in the proposed uncertainty update rule; we show that, under standard validity assumptions on the initial prior bound and disturbance model, the updated uncertainty set remains convex, compact, and nonempty while preserving containment of the true system parameters. To preserve switching safety under controller updates, we introduce a monotone nesting constraint on consecutive certified safe sets, together with automatic fallback to the last certified controller whenever the synthesis LMIs become infeasible. Tightening is data-dependent and is observed when newly acquired measurements are sufficiently informative relative to the current prior. Numerical studies illustrate that informative online measurements can yield practical tightening of the uncertainty set and enlargement of the certified safe sets over successive accepted updates.