Fault-Tolerant Consensus of Single-Integrator Multi-Agent Systems in the Presence of Asynchronous Self-Sensing Function Failures

Noticing that the existing fault-tolerance consensus protocol suitable for synchronous self-sensing function failures (SSSFFs) cannot be directly applied to consensus of single-integrator multiple agent systems (SIMASs), a part of agents of which are subjected to asynchronous SSFFs (ASSFFs), this paper tries to develop a new consensus protocol that has fault tolerance against ASSFFs. First, the network communication topology connectivity restoration (NCTCR) strategy suitable for SSSFFs is used for solving NCTCR under ASSFFs by regarding ASSFFs as multiple SSSFFs. Second, a fault-tolerance consensus protocol suitable for ASSFFs is designed based on the strategy that when the minimum-hop normal neighbor set (MHNNS) of an agent subjected to SSFF changes, its current state is computed by its outdated data. Third, consensus convergence is analyzed, deriving the convergence conditions on the time-varying gain (TVG). It is theoretically proved that consensus is achieved for SIMASs using the NCTCR strategy and the fault-tolerance consensus protocol with the appropriate TVG. Forth, numerical simulation experiments illustrate the validity of the proposed fault-tolerance consensus protocol.