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 mixed-monotone 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.