A Unified Framework for Robust Stabilization and Safety of Uncertain Nonlinear Systems

Abstract

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 control-affine 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 (safe-RCP) for an uncertain system is transformed into a safe-optimal control problem (safe-OCP) 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, a numerical simulation is provided to demonstrate the efficacy of the safe-robust control law.