Integral Concurrent Learning Control Lyapunov Functions and High Order Control Barrier Functions and Application to Adaptive Cruise Control

In this paper, the safety-critical tracking control problem of uncertain nonlinear systems with arbitrary relative degree constraints is addressed. Firstly, an integral concurrent learning high order control barrier function (ICL-HOCBF) is constructed from deriving a class
$\mathcal {K}$
function with time-varying coefficient that depends on the recorded data. On the one hand, it can accommodate unknown parameters in the control vector field and ensure the convergence of parameter estimation errors under finite excitation condition. On the other hand, the proposed ICL-HOCBF by directly enforcing forward invariance of the system containing parameter estimates can approach the boundary of the safety set when CBF constraints are active. In addition, an ICL control Lyapunov function (ICL-CLF) is proposed by using recorded data and online data concurrently, which allows the tracking errors and parameter estimation errors to converge exponentially due to the generation of a negative definite estimation error term in the stability analysis. Meanwhile, this research not only theoretically proves that the developed ICL-CLFs and ICL-HOCBFs can overcome the difficulty of converting state constraints to control constraints caused by uncertainty in the control vector field, and provide strict safety guarantee for uncertain nonlinear safety-critical systems, but also demonstrates the applicability of this method by solving the adaptive cruise control problem of vehicle systems with unknown control coefficients.