The paper introduces a framework for online parameter estimation and uncertainty quantification in adaptive safety-critical control. It leverages continuous-time recursive least squares (RLS) algorithms to generate parameter estimates efficiently. By using objects like zonotopes, set-based estimates are propagated over time, aiding in synthesizing safety-critical controllers for systems with uncertainties. The integration of learning and control raises questions about reliability and safety, addressed through adaptive control schemes with stability guarantees. Safety properties are formalized using set invariance concepts, extended to control systems via control barrier functions (CBFs). Robust adaptive approaches reduce conservatism by assuming known bounds on system parameters. Various uncertainty quantification mechanisms are explored, including set membership identification (SMID) and concurrent learning adaptive control methods. These techniques allow for efficient computation of bounds on parameter estimation errors while accounting for additive disturbances.
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