Distributed sensor fault diagnosis for a formation system with unknown constant time delays

In this paper, a distributed velocity sensor fault diagnosis scheme is presented for a formation of a second-order multi-agent system with unknown constant communication time delays. An existing distributed proportion-derivation (DPD) formation control law is adopted and a delay-independent condition is proposed to guarantee the asymptotical formation stability of the formation system based on the Nyquist stability criterion. Then a distributed fault diagnosis scheme is developed. In each agent, a distributed fault detection residual generator (DFDRG) and a bank of distributed fault isolation residual generators (DFIRGs) are designed based on the closed-loop model of the whole system. Each DFIRG is built up on the basis of a reduced-order unknown input observer (UIO) which is robust to the fault of one neighboring agent. According to the robust relationship between DFIRGs and faults, distributed fault isolation can be achieved. Conditions are presented to guarantee that each agent is able to diagnose faults of itself and its neighbors despite the disturbance of time delays. Finally, outdoor experimental results illustrate the effectiveness of the proposed schemes.