Control Barrier Functions for Safe CPS Under Sensor Faults and Attacks

CPS safety, defined as the system state remaining within a desired safe region, is a critical property in applications including medicine, transportation, and energy. Sensor faults and attacks may cause safety violations by introducing bias into the system state estimation, which in turn leads to erroneous control inputs. In this paper, we propose a class of Fault-Tolerant Control Barrier Functions (FT-CBFs) that provide provable guarantees on the safety of stochastic CPS. Our approach is to maintain a set of state estimators, each of which ignores a subset of sensor measurements that are affected by a particular fault pattern. We then introduce a linear constraint for each state estimator that ensures that the estimated state remains outside the unsafe region, and propose an approach to resolving conflicts between the constraints that may arise due to faults. We present sufficient conditions on the geometry of the safe region and the noise characteristics to provide a desired probability of maintaining safety. We then propose a framework for joint safety and stability by integrating FT-CBFs with Control Lyapunov Functions. Our approach is validated through a numerical study of a wheeled mobile robot.