Consensus and its ℒ₂-gain performance of multi-agent systems with intermittent information transmissions

This article addresses the consensus problem for cooperative multiple agents with nonlinear dynamics on a fixed directed information network, where each agent can only communicate with its neighbours intermittently. A class of control algorithms is first introduced, using only intermittent relative local information. By combining tools from switching systems and Lyapunov stability theory, some sufficient conditions are established for consensus of multi-agent systems without any external disturbances under a fixed strongly connected topology. Theoretical analyses are further provided for consensus of multi-agent systems in the presence of external disturbances. It is shown that a finite ℒ2-gain performance index for the closed-loop multi-agent systems can be guaranteed if the coupling strength of the network is larger than a threshold value determined by the average communication rate and the generalised algebraic connectivity of the strongly connected topology. The results are then extended to consensus with prescribed ℒ2-gain performance with a virtual leader where the underlying topology is not necessarily strong connected or contain a directed spanning tree. Numerical simulations are finally provided to verify and visualise the theoretical analysis. Keywords: multi-agent systemconsensusℒ2-gain performancedirected spanning treevirtual leader Acknowledgements The authors sincerely thank Professor Wei Ren for his inspiring discussions and helpful comments. This work was supported by the Hong Kong Research Grants Council under the GRF Grant CityU 1114/11E, and by the National Nature Science Foundation of China under Grants 60974078, 90916003, 61104153 and the China Postdoctoral Science Foundation under Grants 20100480211 and 201104059.