Convergence Analysis of Classes of Asymmetric Networks of Cucker–Smale Type With Deterministic Perturbations

We discuss two extensions of the Cucker-Smale flocking model with asymmetric coupling weights. The first model assumes a finite collection of autonomous agents aiming to perform a consensus process in the presence of identical internal dynamics. The second model describes a similar population of agents that perform velocity alignment with the restriction of collision-free orbits. Although qualitatively different, we explain how these models can be analyzed under a common framework. Rigorous analysis is conducted toward establishing sufficient conditions for asymptotic flocking to a synchronized motion. Applications of our results are compared with simulations to illustrate the effectiveness of our theoretical estimates.

[1]  Antoine Girard,et al.  Multiagent Flocking Under General Communication Rule , 2014, IEEE Transactions on Control of Network Systems.

[2]  C. Sparrow.  The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors , 1982 .

[3]  Magnus Egerstedt,et al.  Graph Theoretic Methods in Multiagent Networks , 2010, Princeton Series in Applied Mathematics.

[4]  John N. Tsitsiklis,et al.  Convergence of Type-Symmetric and Cut-Balanced Consensus Seeking Systems , 2011, IEEE Transactions on Automatic Control.

[5]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[6]  G. Parisi,et al.  Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study , 2007, Proceedings of the National Academy of Sciences.

[7]  Darald J. Hartfiel,et al.  Markov Set-Chains , 1998 .

[8]  S. Smale,et al.  On the mathematics of emergence , 2007 .

[9]  Frank Allgöwer,et al.  An internal model principle is necessary and sufficient for linear output synchronization , 2011, Autom..

[10]  E. Ott.  Chaos in Dynamical Systems: Contents , 1993 .

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

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

[13]  J. Baras,et al.  Non-linear flocking networks with collision avoidance , 2015, 2015 34th Chinese Control Conference (CCC).

[14]  N. Markley.  Principles of differential equations , 2004 .

[15]  Somarakis Christoforos,et al.  Non-linear flocking networks with collision avoidance , 2015, CCC 2015.

[16]  Felipe Cucker,et al.  A General Collision-Avoiding Flocking Framework , 2011, IEEE Transactions on Automatic Control.

[17]  Seung-Yeal Ha,et al.  A simple proof of the Cucker-Smale flocking dynamics and mean-field limit , 2009 .

[18]  Jesus M. Gonzalez-miranda,et al.  Synchronization And Control Of Chaos: An Introduction For Scientists And Engineers , 2004 .

[19]  John S. Baras,et al.  A simple proof of the continuous time linear consensus problem with applications in non-linear flocking networks , 2015, 2015 European Control Conference (ECC).

[20]  M. Areak,et al.  Passivity as a design tool for group coordination , 2006, 2006 American Control Conference.

[21]  F. Cucker,et al.  Flocking in noisy environments , 2007, 0706.3343.

[22]  Chai Wah Wu,et al.  Synchronization in Coupled Chaotic Circuits and Systems , 2002 .

[23]  David Angeli,et al.  Necessary and sufficient conditions for consensus in nonlinear monotone networks with unilateral interactions , 2017, Autom..

[24]  E. Seneta.  Non-negative Matrices and Markov Chains , 2008 .

[25]  Sébastien Motsch,et al.  Heterophilious Dynamics Enhances Consensus , 2013, SIAM Rev..

[26]  John S. Baras,et al.  Synchronization and collision avoidance in non-linear flocking networks of autonomous agents , 2016, 2016 24th Mediterranean Conference on Control and Automation (MED).

[27]  W. Marsden.  I and J , 2012 .

[28]  L. Moreau,et al.  Stability of continuous-time distributed consensus algorithms , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

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

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

[31]  John S. Baras,et al.  Dynamics of collectives with opinionated agents: The case of scrambling connectivity , 2016, 2016 European Control Conference (ECC).

[32]  Samuel Martin,et al.  Multi-agent flocking under topological interactions , 2013, Syst. Control. Lett..

[33]  P. Olver.  Nonlinear Systems , 2013 .

[34]  John N. Tsitsiklis,et al.  Distributed Asynchronous Deterministic and Stochastic Gradient Optimization Algorithms , 1984, 1984 American Control Conference.

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

[36]  Xiwei Liu.  Distributed nonlinear control algorithms for network consensus , 2010 .