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Mathematical Problems in Engineering
Volume 2018, Article ID 1957070, 11 pages
https://doi.org/10.1155/2018/1957070
Research Article

Predefined-Time Consensus of Nonlinear First-Order Systems Using a Time Base Generator

1Centro de Investigación en Matemáticas (CIMAT), A.C., Computer Science Department, GTO, Mexico
2Tecnologico de Monterrey, Escuela de Ingeniería y Ciencias, Zapopan, Mexico
3Intel Tecnología de México, Multi-Agent Autonomous Systems Lab, Intel Labs, Zapopan, Mexico

Correspondence should be addressed to Héctor M. Becerra; xm.tamic@arreceb.rotceh

Received 16 June 2018; Revised 11 September 2018; Accepted 17 September 2018; Published 9 October 2018

Academic Editor: Ju H. Park

Copyright © 2018 J. Armando Colunga et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. F. Jiang and L. Wang, “Finite-time information consensus for multi-agent systems with fixed and switching topologies,” Physica D: Nonlinear Phenomena, vol. 238, no. 16, pp. 1550–1560, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  2. 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. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. A. Arenas, A. D. Guilera, J. Kurths, Y. Moreno, and C. Zhou, “Synchronization in complex networks,” Physics Reports, vol. 469, no. 3, pp. 93–153, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. H. Shen, J. H. Park, Z.-G. Wu, and Z. Zhang, “Finite-time H synchronization for complex networks with semi-Markov jump topology,” Communications in Nonlinear Science and Numerical Simulation, vol. 24, no. 1–3, pp. 40–51, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  5. H. Shen, S. Huo, J. Cao, and T. Huang, “Generalized state estimation for Markovian coupled networks under round-robin protocol and redundant channels,” IEEE Transactions on Cybernetics, pp. 1–10, 2018. View at Google Scholar · View at Scopus
  6. R. Olfati-Saber, “Flocking for multi-agent dynamic systems: algorithms and theory,” IEEE Transactions on Automatic Control, vol. 51, no. 3, pp. 401–420, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. K.-K. Oh, M.-C. Park, and H.-S. Ahn, “A survey of multi-agent formation control,” Automatica, vol. 53, pp. 424–440, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. W. Ren, “Distributed attitude alignment in spacecraft formation flying,” International Journal of Adaptive Control and Signal Processing, vol. 21, no. 2-3, pp. 95–113, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. Y. Xu, G. Yan, K. Cai, and Z. Lin, “Fast centralized integer resource allocation algorithm and its distributed extension over digraphs,” Neurocomputing, vol. 270, pp. 91–100, 2017. View at Publisher · View at Google Scholar · View at Scopus
  10. Y. Xu, T. Han, K. Cai, Z. Lin, G. Yan, and M. Fu, “A distributed algorithm for resource allocation over dynamic digraphs,” IEEE Transactions on Signal Processing, vol. 65, no. 10, pp. 2600–2612, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. D. Gómez-Gutiérrez and R. De La Guardia, “Chaotic-based synchronization for secure network communications, US Patent 9438422B2,” 2016.
  12. L. Wang and F. Xiao, “Finite-time consensus problems for networks of dynamic agents,” IEEE Transactions on Automatic Control, vol. 55, no. 4, pp. 950–955, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. Z. Zuo and L. Tie, “A new class of finite-time nonlinear consensus protocols for multi-agent systems,” International Journal of Control, vol. 87, no. 2, pp. 363–370, 2014. View at Publisher · View at Google Scholar · View at Scopus
  14. D. Gómez-Gutiérrez, J. Ruiz-León, S. Celikovsky, and J. D. Sánchez-Torres, “A finite-time consensus algorithm with simple structure for fixed networks,” Computación y Sistemas, vol. 22, no. 2, 2018. View at Publisher · View at Google Scholar
  15. R. Olfati-Saber, J. A. Fax, and R. M. Murray, “Consensus and cooperation in networked multi-agent systems,” Proceedings of the IEEE, vol. 95, no. 1, pp. 215–233, 2007. View at Publisher · View at Google Scholar · View at Scopus
  16. W. Ren and R. W. Beard, Distributed Consensus in Multi-Vehicle Cooperative Control, Springer, 2008.
  17. K. Cai and H. Ishii, “Average consensus on arbitrary strongly connected digraphs with time-varying topologies,” Institute of Electrical and Electronics Engineers Transactions on Automatic Control, vol. 59, no. 4, pp. 1066–1071, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  18. Z. Li and Z. Duan, Cooperative Control of Multi-Agent Systems: A Consensus Region Approach, CRC Press, Boca Raton, Fla, USA, 2014.
  19. H. Sayyaadi and M. R. Doostmohammadian, “Finite-time consensus in directed switching network topologies and time-delayed communications,” Scientia Iranica, vol. 18, no. 1, pp. 75–85, 2011. View at Publisher · View at Google Scholar · View at Scopus
  20. M. Franceschelli, A. Giua, A. Pisano, and E. Usai, “Finite-time consensus for switching network topologies with disturbances,” Nonlinear Analysis: Hybrid Systems, vol. 10, pp. 83–93, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  21. J. Cortés, “Finite-time convergent gradient flows with applications to network consensus,” Automatica, vol. 42, no. 11, pp. 1993–2000, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. M. Franceschelli, A. Giua, and A. Pisano, “Finite-time consensus on the median value with robustness properties,” Institute of Electrical and Electronics Engineers Transactions on Automatic Control, vol. 62, no. 4, pp. 1652–1667, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  23. B. Liu, W. Lu, and T. Chen, “Consensus in continuous-time multiagent systems under discontinuous nonlinear protocols,” IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 2, pp. 290–301, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. Y.-K. Zhu, X.-P. Guan, and X.-Y. Luo, “Finite-time consensus for multi-agent systems via nonlinear control protocols,” International Journal of Automation and Computing, vol. 10, no. 5, pp. 455–462, 2013. View at Publisher · View at Google Scholar · View at Scopus
  25. Y. Shang, “Finite-time consensus for multi-agent systems with fixed topologies,” International Journal of Systems Science, vol. 43, no. 3, pp. 499–506, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  26. S. E. Parsegov, A. E. Polyakov, and P. S. Shcherbakov, “Fixed-time consensus algorithm for multi-agent systems with integrator dynamics,” in Proceedings of the 4th IFAC Workshop on Distributed Estimation and Control in Networked Systems, NecSys 2013, pp. 110–115, September 2013. View at Publisher · View at Google Scholar · View at Scopus
  27. Z. Zuo, Q. L. Han, B. Ning, X. Ge, and X. M. Zhang, “An overview of recent advances in fixed-time cooperative control of multiagent systems,” IEEE Transactions on Industrial Informatics, vol. 14, no. 6, pp. 2322–2334, 2018. View at Google Scholar
  28. E. Cruz-Zavala, J. A. Moreno, and L. Fridman, “Uniform Second-Order Sliding Mode Observer for mechanical systems,” in Proceedings of the 2010 11th International Workshop on Variable Structure Systems, VSS 2010, pp. 14–19, Mexico, June 2010. View at Scopus
  29. A. Polyakov, “Nonlinear feedback design for fixed-time stabilization of linear control systems,” IEEE Transactions on Automatic Control, vol. 57, no. 8, pp. 2106–2110, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. C. Yong, X. Guangming, and L. Huiyang, “Reaching consensus at a preset time: single-integrator dynamics case,” in Proceedings of the 31st Chinese Control Conference (CCC), pp. 6220–6225, IEEE, 2012.
  31. Y. Wang, Y. Song, D. J. Hill, and M. Krstic, “Prescribed-time consensus and containment control of networked multiagent systems,” IEEE Transactions on Cybernetics, 2018. View at Google Scholar · View at Scopus
  32. Y. Zhao and Y. Liu, “Specified-time consensus for multi-agent systems,” in Proceedings of the 2017 Chinese Automation Congress (CAC), pp. 732–737, Jinan, October 2017. View at Publisher · View at Google Scholar
  33. Y. Liu, Y. Zhao, W. Ren, and G. Chen, “Appointed-time consensus: accurate and practical designs,” Automatica, vol. 89, pp. 425–429, 2018. View at Google Scholar
  34. J. A. Colunga, C. R. Vázquez, H. M. Becerra, and D. Gómez-Gutiérrez, “Predefined-time consensus using a time base generator (TBG),” in Proceedings of the IFAC Second Conference on Modelling, Identification and Control of Nonlinear Systems (MICNON), vol. 51, pp. 246–253, 2018.
  35. H. M. Becerra, C. R. Vazquez, G. Arechavaleta, and J. Delfin, “Predefined-time convergence control for high-order integrator systems using time base generators,” IEEE Transactions on Control Systems Technology, vol. 26, no. 5, pp. 1866–1873, 2018. View at Publisher · View at Google Scholar
  36. H. K. Khalil and J. W. Grizzle, Nonlinear Systems, vol. 3, Prentice Hall, New Jersey, NJ, USA, 2002.
  37. Q. Ma, S. Xu, F. L. Lewis, B. Zhang, and Y. Zou, “Cooperative output regulation of singular heterogeneous multiagent systems,” IEEE Transactions on Cybernetics, vol. 46, no. 6, pp. 1471–1475, 2016. View at Publisher · View at Google Scholar · View at Scopus
  38. Q. Ma, “Cooperative control of multi-agent systems with unknown control directions,” Applied Mathematics and Computation, vol. 292, pp. 240–252, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  39. A. H. Roger and R. J. Charles, Matrix Analysis, Cambridge University Press, New York, NY, USA, 2nd edition, 2013. View at MathSciNet
  40. W. Yu, G. Wen, G. Chen, and J. Cao, Distributed Cooperative Control of Multi-agent Systems, John Wiley and Sons, 2016.
  41. Z. Li and Z. Duan, “Distributed consensus protocol design for general linear multi-agent systems: a consensus region approach,” IET Control Theory & Applications, vol. 8, no. 18, pp. 2145–2161, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  42. Z. Li, Z. Duan, G. Chen, and L. Huang, “Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 57, no. 1, pp. 213–224, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  43. G. Jarquín, G. Arechavaleta, and V. Parra-Vega, “Time parametrization of prioritized inverse kinematics based on terminal attractors,” in Proceedings of the 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems: Celebrating 50 Years of Robotics, IROS'11, pp. 1612–1617, USA, September 2011. View at Scopus
  44. M. Braun, Differential Equations and Their Applications: An Introduction to Applied Mathematics, vol. 11, Springer Science and Business Media, Third edition, 1983.
  45. H. K. Khalil and J. Grizzle, Nonlinear systems, vol. 3, Prentice hall, Upper Saddle River, New Jersey, NJ, USA, 2002.
  46. J. A. Moreno and M. Osorio, “Strict Lyapunov functions for the super-twisting algorithm,” IEEE Transactions on Automatic Control, vol. 57, no. 4, pp. 1035–1040, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  47. S. Mondal, R. Su, and L. Xie, “Heterogeneous consensus of higher-order multi-agent systems with mismatched uncertainties using sliding mode control,” International Journal of Robust and Nonlinear Control, vol. 27, no. 13, pp. 2303–2320, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  48. Y. Cao and W. Ren, “Finite-time consensus for multi-agent networks with unknown inherent nonlinear dynamics,” Automatica, vol. 50, no. 10, pp. 2648–2656, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus