Robust Control Barrier Functions for Uncertain Parameter-Varying Control Affine Systems With Set-Membership Parameter Estimation

This paper introduces robust control barrier functions for uncertain parameter-varying 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 concave bounding, where the controlled invariance condition remains linear in the control inputs despite nonlinear uncertainties. Moreover, we design alternative robust control Lyapunov functions where the control inputs also appear linearly; thus, these robust control barrier and Lyapunov functions can be coupled to obtain a quadratic program that can be solved online. Additionally, we propose two set-membership parameter estimation methods using polyhedral intersections and interval observers to reduce the conservatism of the robust approaches. Our robust approaches are observed to have comparable performance with adaptive approaches and robust safety guarantees, even when the (robust) adaptive methods may not.