Abstract and Applied Analysis

Consensus of Multiagent Systems with Packet Losses and Communication Delays Using a Novel Control Protocol

Zheping Yan, Di Wu, Wei Zhang, and Yibo Liu

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This paper studies the consensus problem of multiagent system with packet losses and communication delays under directed communication channels. Different from previous research results, a novel control protocol is proposed depending only on periodic sampling and transmitting data in order to be convenient for practical implementation. Due to the randomicity of transmission delays and packet losses, each agent updates its input value asynchronously at discrete time instants with synchronized time stamped information and evolves in continuous time. Consensus conditions for multiagent system consists of three typical dynamics including single integrator, double integrator, and high-order integrator that are all discussed in this paper. It is proved that, for single integrator agents and double integrator systems with only communication delays, consensusability can be ensured through stochastic matrix theory if the designed communication topology contains a directed spanning tree. While, for double integrator agents and high-order integrator agents with packet losses and communication delays, the interval system theory is introduced to prove the consensus of multiagent system under the condition that the designed communication topology is a directed spanning tree. Finally, simulations are carried out to validate the effectiveness of the proposed solutions.

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Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 159609, 13 pages.

First available in Project Euclid: 6 October 2014

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Yan, Zheping; Wu, Di; Zhang, Wei; Liu, Yibo. Consensus of Multiagent Systems with Packet Losses and Communication Delays Using a Novel Control Protocol. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 159609, 13 pages. doi:10.1155/2014/159609. https://projecteuclid.org/euclid.aaa/1412605891

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  • K. Nagatani, Y. Okada, N. Tokunaga et al., “Multirobot exploration for search and rescue missions: a report on map building in RoboCupRescue 2009,” Journal of Field Robotics, vol. 28, no. 3, pp. 373–387, 2011.
  • S. Zhang, J. Yu, A. Zhang, L. Yang, and Y. Shu, “Marine vehicle sensor network architecture and protocol designs for ocean observation,” Sensors, vol. 12, no. 1, pp. 373–390, 2012.
  • S. Iyengar and R. Brooks, Distributed Sensor Networks: Sensor Networking and Applications, CRC Press, 2012.
  • R. Cui, S. S. Ge, B. Voon Ee How, and Y. Sang Choo, “Leader-follower formation control of underactuated autonomous underwater vehicles,” Ocean Engineering, vol. 37, no. 17-18, pp. 1491–1502, 2010.
  • R. Olfati-Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1520–1533, 2004.
  • Y. Zhang and Y.-P. Tian, “Consensus of data-sampled multi-agent systems with random communication delay and packet loss,” IEEE Transactions on Automatic Control, vol. 55, no. 4, pp. 939–943, 2010.
  • W. Ni and D. Cheng, “Leader-following consensus of multi-agent systems under fixed and switching topologies,” Systems and Control Letters, vol. 59, no. 3-4, pp. 209–217, 2010.
  • Y. Cao and W. Ren, “Sampled-data discrete-time coordination algorithms for double-integrator dynamics under dynamic directed interaction,” International Journal of Control, vol. 83, no. 3, pp. 506–515, 2010.
  • W. Ren and R. W. Beard, “Consensus seeking in multiagent systems under dynamically changing interaction topologies,” IEEE Transactions on Automatic Control, vol. 50, no. 5, pp. 655–661, 2005.
  • Y. Gao and L. Wang, “Consensus of multiple double-integrator agents with intermittent measurement,” International Journal of Robust and Nonlinear Control, vol. 20, no. 10, pp. 1140–1155, 2010.
  • P. Lin, Z. Li, Y. Jia, and M. Sun, “High-order multi-agent consensus with dynamically changing topologies and time-delays,” IET Control Theory and Applications, vol. 5, no. 8, pp. 976–981, 2011.
  • P. Lin and Y. Jia, “Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies,” Automatica, vol. 45, no. 9, pp. 2154–2158, 2009.
  • Y. Liu, H. Min, S. Wang, Z. Liu, and S. Liao, “Distributed adaptive consensus for multiple mechanical systems with switching topologies and time-varying delay,” Systems & Control Letters, vol. 64, pp. 119–126, 2014.
  • Y. Gao, J. Ma, M. Zuo, T. Jiang, and J. Duc, “Consensus of discrete-time second-order agents with time-varying topology and time-varying delays,” Journal of the Franklin Institute, vol. 349, no. 8, pp. 2598–2608, 2012.
  • J. Zhu and L. Yuan, “Consensus of high-order multi-agent systems with switching topologies,” Linear Algebra and Its Applications, vol. 443, pp. 105–119, 2014.
  • J. Almeida, C. Silverstre, and A. M. Pascoal, “Continuous time consensus with discrete time communications,” Systems & Control Letters, vol. 61, no. 7, pp. 788–796, 2012.
  • J. Qin, H. Gao, and W. X. Zheng, “Consensus strategy for a class of multi-agents with discrete second-order dynamics,” International Journal of Robust and Nonlinear Control, vol. 22, no. 4, pp. 437–452, 2012.
  • D. Goldin and J. Raisch, “Consensus for agents with double integrator dynamics in heterogeneous networks,” Asian Journal of Control, vol. 15, no. 4, pp. 1–10, 2013.
  • G. Parlangeli, “Collaborative diagnosis and compensation of misbehaving nodes in acyclic consensus networks: analysis and algorithms,” International Journal of Innovative Computing Information and Control, vol. 9, no. 3, pp. 915–938, 2009.
  • X. Su, L. Wu, Shi, and P. :, “Sensor networks with random link failures: distributed filtering for T-S fuzzy systems',” IEEE Transactions on Industrial Informatics, vol. 9, no. 3, pp. 1739–1750, 2013.
  • X. Su, X. Yang, P. Shi, and L. Wu, “Fuzzy control of nonlinear electromagnetic suspension systems,” Mechatronics, 2013.
  • X. Su, P. Shi, L. Wu, and Y.-D. Song, “A novel control design on discrete-time Takagi-Sugeno fuzzy systems with time-varying delays,” IEEE Transactions on Fuzzy Systems, vol. 21, no. 4, pp. 655–671, 2013.
  • J. Yu and L. Wang, “Group consensus in multi-agent systems with switching topologies and communication delays,” Systems and Control Letters, vol. 59, no. 6, pp. 340–348, 2010.
  • B. Iantovics and C. B. Zamfirescu, “ERMS: an evolutionary reorganizing multiagent system,” International Journal of Innovative Computing Information and Control, vol. 9, no. 3, pp. 1171–1188, 2013.
  • L. Wu, X. Su, and P. Shi, “Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems,” Automatica, vol. 48, no. 8, pp. 1929–1933, 2012.
  • R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 2012.
  • J. Wolfowitz, “Products of indecomposable, aperiodic, stochastic matrices,” Proceedings of the American Mathematical Society, vol. 14, no. 5, pp. 733–736, 1963.
  • F. Lewis, Cooperative Control of Multi-Agent Systems: Optimal and Adaptive Design Approaches, Springer, Berlin, Germany, 2013.
  • A. Jadbabaie, J. Lin, and A. S. Morse, “Coordination of groups of mobile autonomous agents using nearest neighbor rules,” IEEE Transactions on Automatic Control, vol. 48, no. 6, pp. 988–1001, 2003.
  • K. Wang, A. N. Michel, and D. Liu, “Necessary and sufficient conditions for the Hurwitz and Schur stability of interval matrices,” IEEE Transactions on Automatic Control, vol. 39, no. 6, pp. 1251–1255, 1994.
  • X. Liao, Q. Luo, Z. Mei, and W. Hu, “Notes on necessary and sufficient conditions of stability, observability and controllability for interval matrices,” Acta Automatica Sinica, vol. 24, no. 6, pp. 829–833, 1998.
  • D.-Q. Zhang, Q.-L. Zhang, and Y.-P. Chen, “Controllability and quadratic stability quadratic stabilization of discrete-time interval systems–-an LMI approach,” IMA Journal of Mathematical Control and Information, vol. 23, no. 4, pp. 413–431, 2006. \endinput