Author

  • Mansoor Saburov

    • International Islamic University Malaysia, Pahang, Malaysia
    • Malaysia
  • Khikmat Saburov

    • Stare Namesti 141, Sokolov, Czech Republic
    • Czechia

Abstract

Multi-Agent Systems (MAS) have attracted more and more interest in recent years. Most researches in the study of discrete-time MAS, presented in the past few years, have considered linear cooperative rules. However, local interactions between agents are more likely to be governed by nonlinear rules. In this paper, we investigate the consensus of discrete-time MAS with time invariant nonlinear cooperative rules. Based on our presented nonlinear model, we show a consensus in the discrete-time MAS. Our model generalizes a classical time invariant De Groot model. It seems that, unlike a linear case, a consensus can be easily achieved a nonlinear case.

Keywords

References

  • Bauso, D., Giarre, L. & Pesenti, R. (2006). Non-linear protocols for optimal distributed consensus in networks of dynamic agents. Systems & Control Letters , 55(11), 918–928.
  • Berger, R. L. (1981). A Necessary and Sufficient Condition for Reaching a Consensus Using DeGroot’s Method. Journal of American Statistics Association, 76 (374), 415-418.
  • DeGroot, M. H. (1974). Reaching a consensus. Journal of American Statistics Association, 69(345), 118-121.
  • Fax, J. A. & Murray, R. M. (2004). Information flow and cooperative control of vehicle formations. IEEE Transactions on Automatic Control, 49(9), 1465–1476.
  • Ganikhodzhaev, R., Mukhamedov, F. & Saburov, M. (2012). G-decompositions of matrices and related problems I. Linear Algebra and its Application, 436, 1344–1366.
  • Jadbabaie, A., Lin, J. & Morse, S. (2003). Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control, 48, 988–1001.
  • Jadbabaie, A., Motee, N., & Barahona, M. (2004). On the stability of the kuramoto model of coupled nonlinear oscillators. Proceedings of the American Control Conference , 4296–4301.
  • Kuramoto, Y. (1984). Chemical oscillations, waves, and turbulence. Springer, Berlin, Germany.
  • Lin, Z., Francis, B. & Maggiore, M. (2007). State agreement for continuous-time coupled nonlinear systems. SIAM Journal on Control and Optimization, 46(1), 288–307.
  • Moreau, L. (2005). Stability of multi-agent systems with time dependent communication links. IEEE Transactions on Automatic Control, 50, 169–182.
  • Olfati-Saber, R. (2006). Flocking for multi-agent dynamic systems: Algorithms and theory. IEEE Transactions on Automatic Control, 51, 401–420.
  • Olfati-Saber, R., Fax, J. A. & Murray, R. M. (2007).Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE , 95(1), 215–233.
  • Papachristodoulou, A. & Jadbabaie, A. (2005). Synchronization in oscillator networks: Switching topologies and nonhomogeneous delays. Proceedings of the 44th IEEE Conference, 5692–5697.
  • Ren, W. & Beard , R. W. (2008). Distributed Consensus in Multi-Vehicle Cooperative Control. London, U.K. Springer-Verlag.
  • Saburov, M. (2007). Onergodic theorem for quadratic stochastic operators. Dokl. Acad. Nauk. Rep. Uzb ., 6, 8-11
  • Saburov, M. (2012). O regularity, transitivity, and Ergodic principle for quadratic stochastic Volterra operators. Proceedings of Academy of Science of Republic Uzbekistan, 3, 9-12.
  • Saburov, M. (2013). Some strange properties of quadratic stochastic Volterra operators. World Applied Sciences Journal , 21, 94-97
  • Strogatz, S. H. (2000). From kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators. Physica D , 143(1), 1–20.
  • Strogatz, S. H. (2003). SYNC: The Emerging Science of Spontaneous Order. Hyperion Press, New York.

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How to Cite

Saburov, M., & Saburov, K. (2013). Reaching a Consensus in Multi-Agent Systems: A Time Invariant Nonlinear Rule. Journal of Education and Vocational Research, 4(5), 130-133. https://doi.org/10.22610/jevr.v4i5.110

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Section

Research Paper

Published

2013-05-30

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