Swarming behaviors in multi-agent systems with nonlinear dynamics.

The dynamic analysis of a continuous-time multi-agent swarm model with nonlinear profiles is investigated in this paper. It is shown that, under mild conditions, all agents in a swarm can reach cohesion within a finite time, where the upper bounds of the cohesion are derived in terms of the parameters of the swarm model. The results are then generalized by considering stochastic noise and switching between nonlinear profiles. Furthermore, swarm models with limited sensing range inducing changing communication topologies and unbounded repulsive interactions between agents are studied by switching system and nonsmooth analysis. Here, the sensing range of each agent is limited and the possibility of collision among nearby agents is high. Finally, simulation results are presented to demonstrate the validity of the theoretical analysis.

[1]  M. Fiedler.  Algebraic connectivity of graphs , 1973 .

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

[3]  Shankar Sastry,et al.  A calculus for computing Filippov's differential inclusion with application to the variable structure control of robot manipulators , 1986, 1986 25th IEEE Conference on Decision and Control.

[4]  Bojan Mohar,et al.  Eigenvalues, diameter, and mean distance in graphs , 1991, Graphs Comb..

[5]  B. Mohar.  THE LAPLACIAN SPECTRUM OF GRAPHS y , 1991 .

[6]  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.

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

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

[9]  Craig W. Reynolds.  Flocks, herds, and schools: a distributed behavioral model , 1998 .

[10]  Xiao Fan Wang,et al.  Synchronization in scale-free dynamical networks: robustness and fragility , 2001, cond-mat/0105014.

[11]  Michael William Newman,et al.  The Laplacian spectrum of graphs , 2001 .

[12]  K. Passino,et al.  A class of attraction/repulsion functions for stable swarm aggregations , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[13]  Kevin M. Passino,et al.  Stability analysis of swarms , 2003, IEEE Trans. Autom. Control..

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

[15]  Daizhan Cheng,et al.  Characterizing the synchronizability of small-world dynamical networks , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  Timothy W. McLain,et al.  Coordination Variables and Consensus Building in Multiple Vehicle Systems , 2004 .

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

[18]  Andrey V. Savkin,et al.  Coordinated collective motion of Groups of autonomous mobile robots: analysis of Vicsek's model , 2004, IEEE Transactions on Automatic Control.

[19]  K.M. Passino,et al.  Stability analysis of social foraging swarms , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[20]  Tianping Chen,et al.  Dynamical behaviors of Cohen-Grossberg neural networks with discontinuous activation functions , 2005, Neural Networks.

[21]  Guanrong Chen,et al.  A time-varying complex dynamical network model and its controlled synchronization criteria , 2004, IEEE Trans. Autom. Control..

[22]  Long Wang,et al.  Virtual Leader Approach to Coordinated Control of Multiple Mobile Agents with Asymmetric Interactions , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

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

[24]  Guanrong Chen,et al.  A time-varying complex dynamical network model and its controlled synchronization criteria , 2005, IEEE Transactions on Automatic Control.

[25]  I. Couzin,et al.  Effective leadership and decision-making in animal groups on the move , 2005, Nature.

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

[27]  Long Wang,et al.  Virtual leader approach to coordinated control of multiple mobile agents with asymmetric interactions , 2006 .

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

[29]  Ji Xiang,et al.  On the V-stability of complex dynamical networks , 2007, Autom..

[30]  Jinde Cao,et al.  Robust Control of Uncertain Stochastic Recurrent Neural Networks with Time-varying Delay , 2007, Neural Processing Letters.

[31]  Chao Liu,et al.  Network synchronizability analysis: the theory of subgraphs and complementary graphs , 2007, ArXiv.

[32]  Jinde Cao,et al.  New communication schemes based on adaptive synchronization. , 2007, Chaos.

[33]  Felipe Cucker,et al.  Emergent Behavior in Flocks , 2007, IEEE Transactions on Automatic Control.

[34]  Jinde Cao,et al.  Global Synchronization of Linearly Hybrid Coupled Networks with Time-Varying Delay , 2008, SIAM J. Appl. Dyn. Syst..

[35]  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..

[36]  Jinde Cao,et al.  Synchronization of switched system and application in communication , 2008 .

[37]  Yu Hongwang,et al.  Collective behavior of swarms with general nonlinear attraction and repulsion functions , 2008, 2008 27th Chinese Control Conference.

[38]  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..

[39]  Jinde Cao,et al.  Global Synchronization in an Array of Delayed Neural Networks With Hybrid Coupling , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[40]  Yufan Zheng,et al.  Aggregation stability of multiple agents with general nonlinear attraction and repulsion forces , 2009, 2009 IEEE International Conference on Control and Automation.

[41]  Wenwu Yu,et al.  Distributed Consensus Filtering in Sensor Networks , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[42]  Wenwu Yu,et al.  On pinning synchronization of complex dynamical networks , 2009, Autom..

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

[44]  Jinde Cao,et al.  Local Synchronization of a Complex Network Model , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[45]  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).

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

[47]  Wenwu Yu,et al.  Consensus in Directed Networks of Agents With Nonlinear Dynamics , 2011, IEEE Transactions on Automatic Control.

[48]  Wenwu Yu,et al.  Distributed Higher Order Consensus Protocols in Multiagent Dynamical Systems , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[49]  Jinde Cao,et al.  Second-order consensus in multi-agent dynamical systems with sampled position data , 2011, Autom..

[50]  Chao Zhai,et al.  A General Alignment Repulsion Algorithm for Flocking of Multi-Agent Systems , 2011, IEEE Transactions on Automatic Control.

[51]  Zhiyong Chen,et al.  No-beacon collective circular motion of jointly connected multi-agents , 2011, Autom..

[52]  Wenwu Yu,et al.  Distributed Adaptive Control of Synchronization in Complex Networks , 2012, IEEE Transactions on Automatic Control.