Event-Triggered Safety-Critical Control for Systems with Unknown Dynamics

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 unmodeled system dynamics, we define adaptive affine control dynamics which are updated based on the error states obtained by real-time sensor measurements. We define an HOCBF for a safety requirement on the unmodeled 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, and derive a condition that guarantees the satisfaction of the HOCBF constraint between events. We illustrate the effectiveness of the proposed framework on adaptive cruise control and compare it with the classical time-driven approach.