Consensus problems in networks of agents with double-integrator dynamics and time-varying delays

In this article, we consider consensus problems in networks of agents with double-integrator dynamics and non-uniform time-varying delays. The agent dynamics is adopted as a typical point mass model based on Newton's law. Without assuming that the weighting factors in the information update schemes are non-negative, we propose two protocols such that both the state and the velocity of agents achieve consensus. An equivalent reduced-order system is introduced to analyse the convergence of the protocols. Some necessary and (or) sufficient conditions for consensus are established in terms of linear matrix inequalities. Simulation results are provided that demonstrate the effectiveness of our theoretical results.

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

[2]  Jorge Cortés,et al.  Finite-time convergent gradient flows with applications to network consensus , 2006, Autom..

[3]  Jiangping Hu,et al.  Leader-following coordination of multi-agent systems with coupling time delays , 2007, 0705.0401.

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

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

[7]  W. Ren.  Consensus strategies for cooperative control of vehicle formations , 2007 .

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

[9]  Randal W. Beard,et al.  A decentralized approach to formation maneuvers , 2003, IEEE Trans. Robotics Autom..

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

[11]  George J. Pappas,et al.  Flocking in Fixed and Switching Networks , 2007, IEEE Transactions on Automatic Control.

[12]  Laura Giarré,et al.  Non-linear protocols for optimal distributed consensus in networks of dynamic agents , 2006, Syst. Control. Lett..

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

[14]  Dimos V. Dimarogonas,et al.  On the Rendezvous Problem for Multiple Nonholonomic Agents , 2007, IEEE Transactions on Automatic Control.

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

[16]  Pierre-Alexandre Bliman,et al.  Average consensus problems in networks of agents with delayed communications , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[17]  Gerardo Lafferriere,et al.  Decentralized control of vehicle formations , 2005, Syst. Control. Lett..

[18]  Guangming Xie,et al.  Average Consensus in Directed Networks of Dynamic Agents with Time-Varying Communication Delays , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

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

[20]  Dimos V. Dimarogonas,et al.  Connectivity preserving distributed swarm aggregation for multiple kinematic agents , 2007, 2007 46th IEEE Conference on Decision and Control.

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

[22]  Long Wang,et al.  Coordinated collective motion in a motile particle group with a leader , 2005 .