Robust Adaptive Safety-Critical Control for Unknown Systems With Finite-Time Elementwise Parameter Estimation

Safety is always one of the most critical principles for a control system. This article investigates a safety-critical control scheme for unknown structured systems by using the control barrier function (CBF) method. Benefiting from the dynamic regressor extension and mixing (DREM), an extended elementwise parameter identification law is utilized to dismiss the uncertainty. It is shown that the proposed control scheme can always ensure safety in the identification process with injected excitation noise. Besides, the elementwise identification process using DREM can minimize the theoretical conservatism of the safe adaptation law compared to other existing adaptive CBF (aCBF) algorithms. The stability of the proposed safe control scheme is proven, where the safety is guaranteed by constructing appropriate forward invariant aCBF. Furthermore, the robustness of our algorithms under bounded disturbances is analyzed. Finally, the proposed framework is tested on two simulation-based examples, including the adaptive cruise control problem where the slope resistance of the following vehicle is robustly estimated in finite time against small disturbances, and the potential crash risk is avoided by our safe control scheme. These examples illustrate the effectiveness of our algorithm.