Persistence based analysis of consensus protocols for dynamic graph networks

This article deals with the consensus problem involving agents with time-varying singularities in the dynamics or communication in undirected graph networks. Existing results provide control laws which guarantee asymptotic consensus. These results are based on the analysis of a system switching between piecewise constant and time-invariant dynamics. This work introduces a new analysis technique relying upon classical notions of persistence of excitation to study the convergence properties of the time-varying multi-agent dynamics. Since the individual edge weights pass through singularities and vary with time, the closed-loop dynamics consists of a non-autonomous linear system. Instead of simplifying to a piecewise continuous switched system as in literature, smooth variations in edge weights are allowed, albeit assuming an underlying persistence condition which characterizes sufficient inter-agent communication to reach consensus. The consensus task is converted to edge-agreement in order to study a stabilization problem to which classical persistence based results apply. The new technique allows precise computation of the rate of convergence to the consensus value.

[1]  Yu-Ping Tian,et al.  Consensus of Multi-Agent Systems With Diverse Input and Communication Delays , 2008, IEEE Transactions on Automatic Control.

[2]  E.M. Atkins,et al.  A survey of consensus problems in multi-agent coordination , 2005, Proceedings of the 2005, American Control Conference, 2005..

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

[4]  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).

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

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

[7]  K. Narendra,et al.  On the Stability of Nonautonomous Differential Equations $\dot x = [A + B(t)]x$, with Skew Symmetric Matrix $B(t)$ , 1977 .

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

[9]  Richard M. Murray,et al.  Information flow and cooperative control of vehicle formations , 2004, IEEE Transactions on Automatic Control.

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

[11]  G. Besancon,et al.  On the PE stabilization of time-varying systems: open questions and preliminary answers , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[12]  Roger Brockett,et al.  The Rate of Descent for Degenerate Gradient Flows , 2000 .

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

[14]  R. Olfati-Saber,et al.  Consensus Filters for Sensor Networks and Distributed Sensor Fusion , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

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

[16]  Tongwen Chen,et al.  Finite-time consensus of multi-agent systems with directed and intermittent links , 2011, Proceedings of the 30th Chinese Control Conference.

[17]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[18]  Yingmin Jia,et al.  Multi-agent consensus with diverse time-delays and jointly-connected topologies , 2011, Autom..

[19]  M. Alighanbari,et al.  Decentralized Task Assignment for Unmanned Aerial Vehicles , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[20]  Murat Arcak,et al.  Passivity as a Design Tool for Group Coordination , 2007, IEEE Transactions on Automatic Control.

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

[22]  Jean-Jacques E. Slotine,et al.  A Study of Synchronization and Group Cooperation Using Partial Contraction Theory , 2004 .

[23]  Maruthi R. Akella,et al.  Persistence filter-based control for systems with time-varying control gains , 2009, Syst. Control. Lett..

[24]  Abraham K. Ishihara,et al.  Stability analysis of degenerate gradient flows via the WKB approximation , 2009, 2009 American Control Conference.

[25]  Mehran Mesbahi,et al.  Edge Agreement: Graph-Theoretic Performance Bounds and Passivity Analysis , 2011, IEEE Transactions on Automatic Control.