Distributed adaptive safe fault-tolerant control for nonlinear systems based on Barrier function

In this paper, a novel adaptive safe fault-tolerant (SFT) controller design framework is proposed to obtain stability with safety guarantee for a class of single systems and a class of interconnected nonlinear systems in the presence of unknown faults. Under the framework, an adaptive fault-tolerant controller for a class of single systems is designed to ensure safety and asymptotic stability simultaneously. For interconnected systems, the neural networks (NNs) is used to parameterize the unknown faults and interconnection terms. Then, a necessary and sufficient condition for the stability of the system is relaxed and a certainty equivalence (CE)-based adaptive controller is proposed to reduce the complexity of control design. Finally, the result of input-to-state safety and uniform ultimate boundedness for the controlled interconnected systems can be obtained. A numerical simulation of the interconnected systems consisting of two inverted pendulums is given to illustrate the effectiveness of the proposed method.