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

Double-integrator multi-agent systems (MASs) might not achieve dynamical consensus, even if only partial agents suffer from self-sensing function failures (SSFFs). SSFFs might be asynchronous in real engineering application. The existing fault-tolerant dynamical consensus protocol suitable for synchronous SSFFs cannot be directly used to tackle fault-tolerant dynamical consensus of double-integrator MASs with partial agents subject to asynchronous SSFFs. Motivated by these facts, this paper explores a new fault-tolerant dynamical consensus protocol suitable for asynchronous SSFFs. First, multi-hop communication together with the idea of treating asynchronous SSFFs as multiple piecewise synchronous SSFFs is used for recovering the connectivity of network topology among all normal agents. Second, a fault-tolerant dynamical consensus protocol is designed for double-integrator MASs by utilizing the history information of an agent subject to SSFF for computing its own state information at the instants when its minimum-hop normal neighbor set changes. Then, it is theoretically proved that if the strategy of network topology connectivity recovery and the fault-tolerant dynamical consensus protocol with proper time-varying gains are used simultaneously, double-integrator MASs with all normal agents and all agents subject to SSFFs can reach dynamical consensus. Finally, comparison numerical simulations are given to illustrate the effectiveness of the theoretical results.