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A Optimization Approach for Consensus in Multi-agent Systems

  • Carlos R. P. dos Santos JuniorEmail author
  • José Reginaldo H. Carvalho
  • Heitor J. Savino
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 148)

Abstract

This work presents a method based on the application of optimization theory to minimize time for consensus in multi-agent systems. More specifically, the Nelder–Mead algorithm, modified for constrained problems, is utilized to compute an optimum matrix gain that minimizes time in an objective function related to consensus time. The paper presents the problem formulation, simulations, and results that prove the efficiency of optimization methods for this class of application.

Keywords

Consensus Multi-agent systems Nelder–Mead optimization 

Notes

Acknowledgements

To SENAI Innovation Institute for Microelectronics, FAPEAM(PROTI MOBI-LIDADE 009/2017), INCT(CNPq 465755/2014-3) and FAPESP(2014/50851-0).

References

  1. 1.
    Ren, W., Beard, R.W., Atkins, E.M.: Information consensus in multivehicle cooperative control. IEEE Control Syst. Mag. 27(2), 71–82 (2007)CrossRefGoogle Scholar
  2. 2.
    Giulietti, F., Pollini, L., Innocenti, M.: Autonomous formation flight. IEEE Control Syst. Mag. 20(6), 34–44 (2000)CrossRefGoogle Scholar
  3. 3.
    Pimenta, L.C.A., Pereira, G.A.S., Michael, N., Mesquita, R.C., Bosque, M.M., Chaimowicz, L., Kumar, V.: Swarm coordination based on smoothed particle hydrodynamics technique. IEEE Trans. Robot. 29(2), 383–399 (2013)CrossRefGoogle Scholar
  4. 4.
    Pimenta, L.C.A., Kumar, V., Mesquita, R.C., Pereira, G.A.S.: Sensing and coverage for a network of heterogeneous robots. In: 2008 47th IEEE Conference on Decision and Control, pp. 3947–3952 (2008)Google Scholar
  5. 5.
    Beard, R.W., Lawton, J., Hadaegh, F.Y.: A coordination architecture for spacecraft formation control. IEEE Trans. Control Syst. Technol. 9(6), 777–790 (2001)CrossRefGoogle Scholar
  6. 6.
    Freitas, E., Carvalho, J.R.H.: Genetic algorithm approach for a class of multi-criteria, multi-vehicle planner of uavs. In: Gaspar-Cunha, A., Henggeler Antunes, C., Coello, C.C. (eds.) Evolutionary Multi-criterion Optimization. Springer International Publishing (2015)Google Scholar
  7. 7.
    Saadat, J., Moallem, P., Koofigar, H.: Training echo estate neural network using harmony search algorithm. Int. J. Artif. Intell. 15(1), 163–179 (2017)Google Scholar
  8. 8.
    Second order intelligent proportional-integral fuzzy control of twin rotor aerodynamic systems. Procedia Comput. Sci. 139, 372–380 (2018); 6th International Conference on Information Technology and Quantitative ManagementGoogle Scholar
  9. 9.
    A self-optimizing mobile network: auto-tuning the network with firefly-synchronized agents. Inf. Sci. 182(1), 77–92 (2012); Nature-Inspired Collective Intelligence in Theory and PracticeGoogle Scholar
  10. 10.
    Lynch, N.A.: Distributed Algorithms. Morgan Kaufmann Publishers Inc., San Francisco (1996)zbMATHGoogle Scholar
  11. 11.
    Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75, 1226–1229 (1995)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Jadbabaie, A., Lin, J., Morse, A.S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Autom. Control 48(6), 988–1001 (2003)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Olfati-Saber, R.: Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Autom. Control 51(3), 401–420 (2006)MathSciNetCrossRefGoogle Scholar
  14. 14.
    dos Santos Junior, C.R.P., Carvalho, J.R.H., Souza, F.O., Savino, H.J.: Exponential consensus with decay rate estimation for heterogeneous multi-agent systems. J. Intell. Robot. Syst. (2018)Google Scholar
  15. 15.
    Luenberger, D.G., Ye, Y.: Linear and Nonlinear Programming, 4th edn. Springer International Publishing (2016)Google Scholar
  16. 16.
    Bazaraa, M.S.: Nonlinear Programming: Theory and Algorithms, 3rd edn. Wiley Publishing (2013)Google Scholar
  17. 17.
    Oliveira, S.L.C., Carvalho, J.R.H., Ferreira, P.A.V.: A convex approach for multi-criteria decision making in hierarchical systems. J. Multi-criteria Decis. Anal. 7(4), 181–192 (1998)CrossRefGoogle Scholar
  18. 18.
    Elfes, A., Bergerman, M., Carvalho, J.R.H., de Paiva, E.C., Ramos, J.J.G., Bueno, S.S.: Air-ground robotic ensembles for cooperative applications: Concepts and preliminary results. In: 1999 International Conference on Field and Service Robotics. Pittsburgh-USA (1999)Google Scholar
  19. 19.
    Lateral control of airship with uncertain dynamics using incremental nonlinear dynamics inversion. IFAC-PapersOnLine 48(19), 69–74 (2015); 11th IFAC Symposium on Robot Control SYROCO 2015CrossRefGoogle Scholar
  20. 20.
    Nelder, J.A., Mead, R.: A simplex method for function minimization. Comput. J. 7, 308–313 (1965)MathSciNetCrossRefGoogle Scholar
  21. 21.
    West, D.B.: Introduction to Graph Theory, 2nd edn. Prentice Hall (2000)Google Scholar
  22. 22.
    Luersen, M., Le Riche, R., Guyon, F.: A constrained, globalized, and bounded Nelder-Mead method for engineering optimization. Struct. Multidiscip. Optim. 27(1–2), 43–54 (2004)CrossRefGoogle Scholar
  23. 23.
    Ren, W., Beard, R.W., Atkins, E.M.: A survey of consensus problems in multi-agent coordination. In: Proceedings of the 2005, American Control Conference, vol. 3, pp. 1859–1864 (2005)Google Scholar
  24. 24.
    Qin, J., Ma, Q., Shi, Y., Wang, L.: Recent advances in consensus of multi-agent systems: a brief survey. IEEE Trans. Ind. Electron. 64(6), 4972–4983 (2017)CrossRefGoogle Scholar
  25. 25.
    Dorri, A., Kanhere, S.S., Jurdak, R.: Multi-agent systems: a survey. IEEE Access 6, 28573–28593 (2018)CrossRefGoogle Scholar
  26. 26.
    Sun, Y.G., Wang, L.: Consensus of multi-agent systems in directed networks with nonuniform time-varying delays. IEEE Trans. Autom. Control 54(7), 1607–1613 (2009).  https://doi.org/10.1109/TAC.2009.2017963CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Carlos R. P. dos Santos Junior
    • 1
    Email author
  • José Reginaldo H. Carvalho
    • 1
  • Heitor J. Savino
    • 2
  1. 1.Institute of ComputingFederal University of AmazonasManausBrazil
  2. 2.Institute of ComputingFederal University of AlagoasMaceióBrazil

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