Avoiding Congestion in Cluster Consensus of the Second-Order Nonlinear Multiagent Systems

In order to avoid congestion in the second-order nonlinear leader-following multiagent systems over capacity-limited paths, an approach called cluster lag consensus is proposed, which means that the agents in different clusters will pass through the same positions with the same velocities but lag behind the leader at different times. Lyapunov functionals and matrix theory are applied to analyze such cluster lag consensus. It is shown that when the graphic roots of clusters are influenced by the leader and the intracoupling of cluster agents is larger than a threshold, the cluster lag consensus can be achieved. Furthermore, the cluster lag consensus with a time-varying communication topology is investigated. Finally, an illustrative example is presented to demonstrate the effectiveness of the theoretical results. In particular, when the physical sizes of the agents are taken into consideration, it is shown that with a rearrangement and a position transformation, the multiagent system will reach cluster lag consensus in the new coordinate system. This means that all agents in the same cluster will reach consensus on the velocity, but their positions may be different and yet their relative positions converge to a constant asymptotically.

[1]  Huijun Gao,et al.  Cluster synchronization in directed networks of partial-state coupled linear systems under pinning control , 2014, Autom..

[2]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[3]  Rainer Hegselmann,et al.  Opinion dynamics and bounded confidence: models, analysis and simulation , 2002, J. Artif. Soc. Soc. Simul..

[4]  Guangming Xie,et al.  Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays , 2008, Syst. Control. Lett..

[5]  Zhen Wang,et al.  Second-order group consensus for multi-agent systems via pinning leader-following approach , 2014, J. Frankl. Inst..

[6]  Xinghuo Yu,et al.  On the cluster consensus of discrete-time multi-agent systems , 2011, Syst. Control. Lett..

[7]  Guoqiang Hu,et al.  Pinning Synchronization of Directed Networks With Switching Topologies: A Multiple Lyapunov Functions Approach , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[8]  Guanrong Chen,et al.  Pinning Control of Lag-Consensus for Second-Order Nonlinear Multiagent Systems , 2017, IEEE Transactions on Cybernetics.

[9]  Sung Jin Yoo,et al.  Distributed Consensus Tracking for Multiple Uncertain Nonlinear Strict-Feedback Systems Under a Directed Graph , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[10]  Xiwei Liu,et al.  Cluster Synchronization in Directed Networks Via Intermittent Pinning Control , 2011, IEEE Transactions on Neural Networks.

[11]  Richard M. Murray,et al.  INFORMATION FLOW AND COOPERATIVE CONTROL OF VEHICLE FORMATIONS , 2002 .

[12]  Wei Xing Zheng,et al.  Consensus of multiple second-order vehicles with a time-varying reference signal under directed topology , 2011, Autom..

[13]  Tianping Chen,et al.  New approach to synchronization analysis of linearly coupled ordinary differential systems , 2006 .

[14]  Jürgen Kurths,et al.  Consensus over directed static networks with arbitrary finite communication delays. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Wenwu Yu,et al.  Second-Order Consensus for Multiagent Systems With Directed Topologies and Nonlinear Dynamics , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[16]  Wei Ren,et al.  Information consensus in multivehicle cooperative control , 2007, IEEE Control Systems.

[17]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[18]  Long Wang,et al.  Group consensus in multi-agent systems with switching topologies and communication delays , 2010, Syst. Control. Lett..

[19]  Hyo-Sung Ahn,et al.  A survey of multi-agent formation control , 2015, Autom..

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

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

[22]  V. Filipovic,et al.  Global exponential stability of switched systems , 2011 .

[23]  Wei Wu,et al.  Cluster Synchronization of Linearly Coupled Complex Networks Under Pinning Control , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  Jorge Cortes,et al.  Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms , 2009 .

[25]  Daniel W. C. Ho,et al.  Convergence Rate for Discrete-Time Multiagent Systems With Time-Varying Delays and General Coupling Coefficients , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[26]  J. Hendrickx,et al.  Rigid graph control architectures for autonomous formations , 2008, IEEE Control Systems.

[27]  Naomi Ehrich Leonard,et al.  Collective Motion, Sensor Networks, and Ocean Sampling , 2007, Proceedings of the IEEE.

[28]  Guo-Xing Wen,et al.  Adaptive Consensus Control for a Class of Nonlinear Multiagent Time-Delay Systems Using Neural Networks , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[29]  Junping Du,et al.  Tracking Algorithms for Multiagent Systems , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[30]  Junping Du,et al.  Finite-Time Consensus for Multiagent Systems With Cooperative and Antagonistic Interactions , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[31]  L. Chua,et al.  Synchronization in an array of linearly coupled dynamical systems , 1995 .

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

[33]  L. Chua.  The Genesis of Chua's circuit , 1992 .

[34]  Sonia Martínez,et al.  Coverage control for mobile sensing networks , 2002, IEEE Transactions on Robotics and Automation.

[35]  Wenwu Yu,et al.  An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination , 2012, IEEE Transactions on Industrial Informatics.

[36]  Ella M. Atkins,et al.  Distributed multi‐vehicle coordinated control via local information exchange , 2007 .

[37]  Tingwen Huang,et al.  Second-Order Global Consensus in Multiagent Networks With Random Directional Link Failure , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[38]  Xinghuo Yu,et al.  Second-order tracking control for leader-follower multi-agent flocking in directed graphs with switching topology , 2011, Syst. Control. Lett..

[39]  Dirk Aeyels,et al.  Cluster formation in a time-varying multi-agent system , 2011, Autom..

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

[41]  Tianping Chen,et al.  Partial synchronization in linearly and symmetrically coupled ordinary differential systems , 2009 .

[42]  Tingwen Huang,et al.  Second-Order Consensus Seeking in Multi-Agent Systems With Nonlinear Dynamics Over Random Switching Directed Networks , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[43]  Frank L. Lewis,et al.  Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics , 2012, Autom..

[44]  Changchun Hua,et al.  Finite-time consensus tracking of second-order multi-agent systems via nonsingular TSM , 2014 .

[45]  Guangming Xie,et al.  Consensus control for a class of networks of dynamic agents , 2007 .

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