Exponential consensus of general linear multi-agent systems under directed dynamic topology

This paper aims to investigate the consensus control of generic linear multi-agent systems (MASs) under directed dynamic topology. Nonnegative matrix theory, in particular the product properties of infinite row-stochastic matrices, which are widely used for multiple integrator agents, is explored to deal with the convergence analysis of generic linear MASs. It is finally shown that the exponential consensus can be reached under very relaxed conditions, i.e., the directed interaction topology is only required to be repeatedly jointly rooted and the exponentially unstable mode of each individual system is weak enough. Moreover, a least convergence rate and a bound for the unstable mode of the individual agent system, both of which are independent of the switching mode, can be explicitly specified.

[1]  Luc Moreau,et al.  Stability of multiagent systems with time-dependent communication links , 2005, IEEE Transactions on Automatic Control.

[2]  Manfredi Maggiore,et al.  Necessary and sufficient graphical conditions for formation control of unicycles , 2005, IEEE Transactions on Automatic Control.

[3]  Kai Cai,et al.  Quantized Consensus and Averaging on Gossip Digraphs , 2011, IEEE Transactions on Automatic Control.

[4]  Hyungbo Shim,et al.  Consensus of high-order linear systems using dynamic output feedback compensator: Low gain approach , 2009, Autom..

[5]  Long Wang,et al.  Sampled-Data Based Consensus of Continuous-Time Multi-Agent Systems With Time-Varying Topology , 2011, IEEE Transactions on Automatic Control.

[6]  Long Wang,et al.  Asynchronous Consensus in Continuous-Time Multi-Agent Systems With Switching Topology and Time-Varying Delays , 2006, IEEE Transactions on Automatic Control.

[7]  Yu-Ping Tian,et al.  Maximum Allowable Loss Probability for Consensus of Multi-Agent Systems Over Random Weighted Lossy Networks , 2012, IEEE Transactions on Automatic Control.

[8]  Huijun Gao,et al.  A Sufficient Condition for Convergence of Sampled-Data Consensus for Double-Integrator Dynamics With Nonuniform and Time-Varying Communication Delays , 2012, IEEE Transactions on Automatic Control.

[9]  Ji-Feng Zhang,et al.  Necessary and Sufficient Conditions for Consensusability of Linear Multi-Agent Systems , 2010, IEEE Transactions on Automatic Control.

[10]  Daizhan Cheng,et al.  Leader-following consensus of multi-agent systems under fixed and switching topologies , 2010, Syst. Control. Lett..

[11]  Ming Cao,et al.  Clustering in diffusively coupled networks , 2011, Autom..

[12]  Daizhan Cheng,et al.  Consensus of multi-agent linear dynamic systems† , 2008 .

[13]  Brian D. O. Anderson,et al.  Agreeing Asynchronously , 2008, IEEE Transactions on Automatic Control.

[14]  Brian D. O. Anderson,et al.  Reaching a Consensus in a Dynamically Changing Environment: Convergence Rates, Measurement Delays, and Asynchronous Events , 2008, SIAM J. Control. Optim..

[15]  Wenwu Yu,et al.  Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems , 2010, Autom..

[16]  Chai Wah Wu,et al.  Synchronization and convergence of linear dynamics in random directed networks , 2006, IEEE Transactions on Automatic Control.

[17]  Guanghui Wen,et al.  Consensus in multi‐agent systems with communication constraints , 2012 .

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

[19]  Manfredi Maggiore,et al.  State Agreement for Continuous-Time Coupled Nonlinear Systems , 2007, SIAM J. Control. Optim..

[20]  Wei Xing Zheng,et al.  Exponential Synchronization of Complex Networks of Linear Systems and Nonlinear Oscillators: A Unified Analysis , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[21]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[22]  J. Wolfowitz.  Products of indecomposable, aperiodic, stochastic matrices , 1963 .

[23]  Tao Li,et al.  Consensus Conditions of Multi-Agent Systems With Time-Varying Topologies and Stochastic Communication Noises , 2010, IEEE Transactions on Automatic Control.

[24]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[25]  Sezai Emre Tuna,et al.  Conditions for Synchronizability in Arrays of Coupled Linear Systems , 2008, IEEE Transactions on Automatic Control.

[26]  E. Seneta,et al.  Towards consensus: some convergence theorems on repeated averaging , 1977, Journal of Applied Probability.

[27]  Randal W. Beard,et al.  Distributed Consensus in Multi-vehicle Cooperative Control - Theory and Applications , 2007, Communications and Control Engineering.

[28]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[29]  Lihua Xie,et al.  Network Topology and Communication Data Rate for Consensusability of Discrete-Time Multi-Agent Systems , 2011, IEEE Transactions on Automatic Control.

[30]  Sezai Emre Tuna,et al.  Synchronizing linear systems via partial-state coupling , 2008, Autom..