Dynamic regressor extension and mixing control Lyapunov functions and high-order control Barrier functions

Abstract

This paper studies the safety-critical tracking control problem for unknown structured systems with bounded disturbances and high relative degree. Firstly, a dynamic regressor extension and mixing high-order control barrier function (DREM-HOCBF) is constructed with a DREM-based robust finite-time parameter identification law. Our approach directly enforces forward invariance of the system containing parameter estimates and worst-case estimation errors to ensure system safety against parameterised uncertainty. Due to DREM, this method can approach the safety set boundary and reduce the conservatism. Meanwhile, it's also applicable to higher relative degree constraints that are more common in actual systems. Then, a DREM control Lyapunov function (DREM-CLF) that leverages the same worst-case estimation errors is proposed to guarantee that the tracking errors converge exponentially. Moreover, the method's robustness against bounded disturbances is considered. Finally, the feasibility of the developed method is verified via an adaptive cruise control (ACC) problem with unknown parameters and bounded disturbances.