Fault-tolerant safe control for water networks: A backstepping neural control barrier function approach

As a typical nonlinear process control infrastructure, the safety and reliability of drinking water transport systems (DWTS) are affected by various factors, including their complex interconnected structures and external environments. This paper proposes a fault-tolerant control scheme for DWTS that ensures their states remain within safe boundaries despite the presence of disturbances, uncertainties and faults. Firstly, considering the impacts of random consumer behavior, unpredictable process and actuator faults, the DWTS is modeled as an interconnected stochastic nonlinear system. Secondly, combining the backstepping technique with control barrier functions, a sufficient and necessary condition for guaranteeing system safety is derived. Thirdly, by minimizing a loss function constructed based on dynamic programming, we synthesize a distributed controller using neural networks and theoretically prove the safety guarantees provided by our approach. Lastly, simulations are conducted to validate the effectiveness of the proposed approach on our benchmark water transport system.