Control schemes based on the wave equation for consensus in multi-agent systems with double-integrator dynamics

In this paper, we consider the problem of driving a group of agents communicating through an undirected and weighted network towards a consensus point. We assume that agents obey to double-integrator dynamics and study decentralized control schemes for consensus of the position variables. In particular we revisit control policies proposed in [1] and [2] in the unified framework of Partial difference Equations over graphs and highlight the link between the closed-loop system dynamics and the damped wave equation describing the motion of a free elastic beam.

[1]  George J. Pappas,et al.  Stable flocking of mobile agents part I: dynamic topology , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[2]  A. Bensoussan,et al.  Difference equations on weighted graphs , 2005 .

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

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

[5]  T. Carroll,et al.  MASTER STABILITY FUNCTIONS FOR SYNCHRONIZED COUPLED SYSTEMS , 1999 .

[6]  V. Thomée,et al.  Finite-Element Methods for a Strongly Damped Wave Equation , 1991 .

[7]  G. F.,et al.  From individuals to aggregations: the interplay between behavior and physics. , 1999, Journal of theoretical biology.

[8]  George J. Pappas,et al.  Stable flocking of mobile agents, part I: fixed topology , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

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

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

[11]  Long Wang,et al.  Coordination of Multiple Dynamic Agents with Asymmetric Interactions , 2005, Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005..

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

[13]  Ella M. Atkins,et al.  Second-order Consensus Protocols in Multiple Vehicle Systems with Local Interactions , 2005 .

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

[15]  Béla Bollobás,et al.  Modern Graph Theory , 2002, Graduate Texts in Mathematics.

[16]  Wei Ren,et al.  Second-order Consensus Algorithm with Extensions to Switching Topologies and Reference Models , 2007, 2007 American Control Conference.

[17]  M. Spong,et al.  Agreement with non-uniform information delays , 2006, 2006 American Control Conference.

[18]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[19]  L. Pecora.  Synchronization conditions and desynchronizing patterns in coupled limit-cycle and chaotic systems , 1998 .

[20]  Giancarlo Ferrari-Trecate,et al.  Analysis of coordination in multi-agent systems through partial difference equations , 2006, IEEE Transactions on Automatic Control.