On Swarm Stability of Linear Time-Invariant Descriptor Compartmental Networks

Swarm stability is studied for descriptor compartmental networks with linear time-invariant protocol. Compartmental network is a specific type of dynamical multi-agent system. Necessary and sufficient conditions for both consensus and marginal swarm stability are presented, which require a joint matching between the interactive dynamics of nearest neighbouring vertices and the Laplacian spectrum of the overall network topology. Three numerical instances are provided to verify the theoretical results.

[1]  N. Cai,et al.  Swarm Stability Analysis of Nonlinear Dynamical Multi-Agent Systems via Relative Lyapunov Function , 2014 .

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

[3]  Yisheng Zhong,et al.  Brief paper swarm stability of high-order linear time-invariant swarm systems , 2011 .

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

[5]  Zongying Shi,et al.  Admissible consensus and consensualization of high-order linear time-invariant singular swarm systems , 2012 .

[6]  Xiao Fan Wang,et al.  Flocking of Multi-Agents With a Virtual Leader , 2009, IEEE Trans. Autom. Control..

[7]  G. Duan.  Analysis and Design of Descriptor Linear Systems , 2010 .

[8]  Z. Duan,et al.  H∞ consensus regions of multi-agent systems , 2010, Proceedings of the 29th Chinese Control Conference.

[9]  Yang Liu,et al.  Stability analysis of one-dimensional asynchronous swarms , 2003, IEEE Trans. Autom. Control..

[10]  Yisheng Zhong,et al.  Delay-dependent admissible consensualization for singular time-delayed swarm systems , 2012, Syst. Control. Lett..

[11]  Mohammad Saleh Tavazoei,et al.  Fractional-order linear time invariant swarm systems: asymptotic swarm stability and time response analysis , 2013 .

[12]  Cai Ning,et al.  On uniform consensus of linear multi-agent systems with time-varying graph topologies , 2013, Proceedings of the 32nd Chinese Control Conference.

[13]  Kai Jin,et al.  Stability of synchronized distributed control of discrete swarm structures , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

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

[15]  Tucker R. Balch,et al.  Behavior-based formation control for multirobot teams , 1998, IEEE Trans. Robotics Autom..

[16]  F. Xiao,et al.  Consensus problems for high-dimensional multi-agent systems , 2007 .

[17]  Tianguang Chu,et al.  Self-organized motion in anisotropic swarms , 2003 .

[18]  N. Cai,et al.  Swarm Stability of Compartmental Networks with Linear Time-Invariant High-Order Dynamical Protocol , 2011, 2011 International Conference on Business Computing and Global Informatization.

[19]  Yisheng Zhong,et al.  Containment analysis and design for high-order linear time-invariant singular swarm systems with time delays , 2012, Proceedings of the 31st Chinese Control Conference.

[20]  John J. Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities , 1999 .

[21]  Jörg Widmer,et al.  In-network aggregation techniques for wireless sensor networks: a survey , 2007, IEEE Wireless Communications.

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

[23]  Shugen Ma,et al.  Multi-agent supporting systems (MASS): control with centralized estimator of disturbance , 1994, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'94).

[24]  Lei Zhou,et al.  Stability analysis of switched linear singular systems , 2013, Autom..

[25]  H. Knudsen,et al.  Controllability and observability of linear time-invariant compartmental models , 1978 .

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

[27]  Wei Li.  Stability Analysis of Swarms With General Topology , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[28]  Guo-Ping Liu,et al.  Necessary and Sufficient Consensus Conditions of Descriptor Multi-agent Systems , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.