Model decomposition-based fault-tolerant control for interconnected wave partial differential equation systems

Abstract

The fault-tolerant control (FTC) issue for a class of interconnected wave-distributed parameter systems is addressed by using the inclusion principle. Both subsystem faults and coupling faults are considered. First, the original system is expanded into an equivalent decoupled system. The main structure of the expanded system consists of multiple pair-wise subsystems. Second, the pair-wise fault-tolerant controllers are designed to stabilise the pair-wise subsystems, which can compensate for the effects of subsystem faults and major coupling faults. Third, a coordinated fault-tolerant controller with a suitable coordinated compensator for the expanded system is constructed according to the pair-wise fault-tolerant controllers of all subsystems. The coordinated compensator is used to compensate for the effects of other minor interconnections and coupling faults, and the coordinated controller is designed for the expanded system. Furthermore, the fault-tolerant controller is obtained to guarantee asymptotical stability of the faulty interconnected wave system by satisfying the contraction condition. The numerical experiments are presented to illustrate the effectiveness of the FTC method.