  This paper addresses the problem of safety-critical control for systems with
unknown dynamics. It has been shown that stabilizing affine control systems to
desired (sets of) states while optimizing quadratic costs subject to state and
control constraints can be reduced to a sequence of quadratic programs (QPs) by
using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs).
Our recently proposed High Order CBFs (HOCBFs) can accommodate constraints of
arbitrary relative degree. One of the main challenges in this approach is
obtaining accurate system dynamics, which is especially difficult for systems
that require online model identification given limited computational resources
and system data. In order to approximate the real unmodelled system dynamics,
we define adaptive affine control dynamics which are updated based on the error
states obtained by real-time sensor measurements. We define a HOCBF for a
safety requirement on the unmodelled system based on the adaptive dynamics and
error states, and reformulate the safety-critical control problem as the above
mentioned QP. Then, we determine the events required to solve the QP in order
to guarantee safety. We also derive a condition that guarantees the
satisfaction of the HOCBF constraint between events. We illustrate the
effectiveness of the proposed framework on an adaptive cruise control problem
and compare it with the classical time-driven approach.
