Fault-Tolerant Finite-Time Consensus of Multi-Agent Systems Under Asynchronous Self-Sensing Function Failures

This article investigates fault-tolerant finite-time consensus (FTC) problems of single/double-integrator multi-agent systems (MASs) with partial agents subject to asynchronous self-sensing function failures (SSFFs). First, the strategy named DRMNNS is developed to recover the connectivity of network topology among normal agents by converting asynchronous SSFFs into multiple piecewise synchronous SSFFs and using multi-hop communication (MHC) together with agents subject to SSFFs as routing nodes. Second, by employing the state and input information of all agents in minimum-hop normal neighbor set (MHNNS) of an agent subject to SSFF and utilizing the history information of the agent subject to SSFF for computing its state information at the instants when its MHNNS changes, two switching fault-tolerant FTC protocols with single/double time-varying gains are designed, respectively, for single/double-integrator MASs. Third, convergence analysis is carried out by separately investigating the closed-loop dynamics of normal agents and the open-loop dynamics of agents subject to SSFFs, and convergence conditions in terms of time-varying gains are derived. It turns out that single/double-integrator MASs under asynchronous SSFFs using the proposed DRMNNS strategy and two fault-tolerant FTC protocols with proper time-varying gains can reach FTC/finite-time dynamical consensus (FTDC), respectively. Finally, comparison numerical simulations are provided to illustrate the effectiveness of the theoretical results.