A Unified Framework for Attack-Resilient CLF-CBF Quadratic Programs for Nonlinear Control-Affine Systems

Abstract

This letter introduces attack-resilient Control Lyapunov Functions (AR-CLFs) and attack-resilient Control Barrier Functions (AR-CBFs) for nonlinear control-affine systems subject to control-input false data injection attacks (FDIA) satisfying an at-most-exponentially growing envelope. The proposed framework embeds a unified adaptive compensation term into both the CLF decrease and CBF safety constraints. In contrast to input-to-state stability/safety (ISS/ISSf)-based methods that certify disturbance-dependent enlarged safe sets, the proposed approach enables finite-time recovery to the nominal safe set without requiring a prior magnitude bound on the FDIA, relying instead on a growth-rate characterization used for analysis and an online gain tuning law that regulates the compensation term. A unified quadratic program (QP) is developed to enforce the AR-CLF and AR-CBF conditions simultaneously, guaranteeing uniformly ultimately bounded (UUB) stability and uniform ultimate safety (UUS) under unbounded FDIA. Numerical results demonstrate improved resilience compared to existing ISS-CLF, ISSf-CBF, and robust CLF-CBF-QP approaches.