Consensus Problems in Networks of Agents under Nonlinear Protocols with Directed Interaction Topology

The purpose of this short paper is to provide a theoretical analysis for the consensus problem under nonlinear protocols. A main contribution of this work is to generalize the previous consensus problems under nonlinear protocols for networks with undirected graphs to directed graphs (information flow). Our theoretical result is that if the directed graph is strongly connected and the nonlinear protocol is strictly increasing, then consensus can be realized. Some simple examples are also provided to demonstrate the validity of our theoretical result.

[1]  Kevin M. Passino,et al.  Stability analysis of swarms , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[2]  Reza Olfati-Saber,et al.  Flocking for multi-agent dynamic systems: algorithms and theory , 2006, IEEE Transactions on Automatic Control.

[3]  R. Murray,et al.  Consensus protocols for networks of dynamic agents , 2003, Proceedings of the 2003 American Control Conference, 2003..

[4]  P. Hartman.  Ordinary Differential Equations , 1965 .

[5]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[6]  C. Wu.  Synchronization in networks of nonlinear dynamical systems coupled via a directed graph , 2005 .

[7]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[8]  Tianping Chen,et al.  Exponential Synchronization of Nonlinear Coupled Dynamical Networks , 2007, Int. J. Bifurc. Chaos.

[9]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[10]  N. G. Parke,et al.  Ordinary Differential Equations. , 1958 .

[11]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[12]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.