Consensus of Networked Multi-agent Systems with Delays and Fractional-Order Dynamics

Abstract

AbstractThis chapter is devoted to studying the consensus problem of networked multi-agent systems with delays and fractional-order dynamics. The effects of input delay, communication delay, fractional-order dynamics and directed information flow on the consensus behavior of networked multi-agent systems are systematically studied. We find that consensus is very robust against communication delays in both integer-order systems and fractional-order systems with fractional-order α ∈ (0, 1]. One well-informed leader is proved to be enough for the regulation of all agents’ final state, even when the external signal is very weak. By using the generalized Nyquist stability criterion, a necessary and sufficient condition is derived to ensure the consensus of fractional-order systems with identical input delays over directed networks. Furthermore, when the interaction topology is undirected, consensus condition of fractional-order systems with heterogeneous input delays is explicitly given. Based on frequency-domain approach, sufficient conditions are obtained to ensure the consensus of the fractional-order systems with simultaneously nonuniform input and communication delays.KeywordsCommunication DelayConsensus ProblemInput DelayConsensus ProtocolCaputo DefinitionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.