Abstract Control barrier functions (CBFs) are widely employed to ensure safety in nonlinear systems; however, the presence of uncertainties can impact their effectiveness, leading to safety violations. In this context, we present the design of a safe-robust control law that unifies the objective of robust stabilization and safety for a nonlinear system in the presence of mismatched uncertainty. This unified framework is achieved through a switching strategy that operates based on safety requirements, resulting in a slightly larger CBF. Thereby, guaranteeing the forward invariance of a larger CBF ensures that states avoid the actual unsafe region. To derive the proposed control law, the safe-robust control problem for an uncertain system is transformed into a safe-optimal control problem for auxiliary dynamics with appropriate cost. Furthermore, we draw connections between two prominent robust control techniques and show how safety can be integrated using the proposed approach. Finally, numerical simulation is provided to demonstrate the efficacy of the safe-robust control law.
Tiwari et al. (Sat,) studied this question.