Robust Control Barrier Functions for Control Affine Systems with Time-Varying Parametric Uncertainties

This paper introduces robust control barrier functions for uncertain control affine systems, where the (parametric) uncertainties can be time-varying and nonlinearly affecting the system dynamics and/or safety sets. In particular, we propose two methods based on mixedmonotone decomposition and robust optimization where the controlled invariance condition remains linear in the control inputs despite nonlinear uncertainties. We show that these functions guarantee the robust controlled invariance of a given parameter-dependent safety set while existing adaptive approaches may not. Moreover, we propose alternative robust control Lyapunov functions where the control inputs also appear linearly; thus, these robust control barrier and Lyapunov functions can be coupled and remain a quadratic program that can be solved online. Finally, we demonstrate using two illustrative examples that our approaches have comparable performance with adaptive approaches while guaranteeing robust safety. Copyright (c) 2023 The Authors.