Fault-tolerant control for a class of linear interconnected hyperbolic systems by boundary feedback

This paper considers a fault-tolerant control problem for a class of interconnected linear hyperbolic partial differential equation systems. Both subsystem faults and coupling faults are considered. Firstly, the well-posedness of the faulty system is analyzed by using semigroup theory. Secondly, for the fault-free case, a stabilizing boundary feedback control based on small-gain theorem is proposed. Consequently, in the presence of faults, fault recoverability conditions are established that maintain the stability of the faulty systems. The fault-tolerant control strategies are also provided. A heat exchanger example is taken to illustrate the effectiveness and practicality of the proposed methods.