  Safety is one of the most important properties of control systems. Sensor
faults and attacks and actuator failures may cause errors in the sensor
measurements and system dynamics, which leads to erroneous control inputs and
hence safety violations. In this paper, we improve the robustness against
sensor faults and actuator failures by proposing a class of Fault-Tolerant
Control Barrier Functions (FT-CBFs) for nonlinear systems. Our approach
maintains a set of state estimators according to fault patterns and
incorporates CBF-based linear constraints for each state estimator. We then
propose a framework for joint safety and stability by integrating FT-CBFs with
Control Lyapunov Functions. With a similar philosophy of utilizing redundancy,
we proposed High order CBF-based approach to ensure safety when actuator
failures occur. We propose a sum-of-squares (SOS) based approach to verify the
feasibility of FT-CBFs for both sensor faults and actuator failures. We
evaluate our approach via two case studies, namely, a wheeled mobile robot
(WMR) system in the presence of a sensor attack and a Boeing 747 lateral
control system under actuator failures.
