Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
156 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Optimal Pinning Control for Synchronization over Temporal Networks (2403.09127v1)

Published 14 Mar 2024 in eess.SY and cs.SY

Abstract: In this paper, we address the finite time synchronization of a network of dynamical systems with time-varying interactions modeled using temporal networks. We synchronize a few nodes initially using external control inputs. These nodes are termed as pinning nodes. The other nodes are synchronized by interacting with the pinning nodes and with each other. We first provide sufficient conditions for the network to be synchronized. Then we formulate an optimization problem to minimize the number of pinning nodes for synchronizing the entire network. Finally, we address the problem of maximizing the number of synchronized nodes when there are constraints on the number of nodes that could be pinned. We show that this problem belongs to the class of NP-hard problems and propose a greedy heuristic. We illustrate the results using numerical simulations.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (35)
  1. J. Zhao, D. J. Hill, and T. Liu, “Synchronization of complex dynamical networks with switching topology: A switched system point of view,” Automatica, vol. 45, no. 11, pp. 2502–2511, 2009.
  2. D. Liu and D. Ye, “Edge-based decentralized adaptive pinning synchronization of complex networks under link attacks,” IEEE Transactions on Neural Networks and Learning Systems, vol. 33, no. 9, pp. 4815–4825, 2021.
  3. C. S. Peskin, “Mathematical aspects of heart physiology,” Courant Inst. Math, 1975.
  4. X. Li and G. Chen, “Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 50, no. 11, pp. 1381–1390, 2003.
  5. F. Sorrentino, M. Di Bernardo, F. Garofalo, and G. Chen, “Controllability of complex networks via pinning,” Physical Review E, vol. 75, no. 4, p. 046103, 2007.
  6. Y. Tang, F. Qian, H. Gao, and J. Kurths, “Synchronization in complex networks and its application–a survey of recent advances and challenges,” Annual Reviews in Control, vol. 38, no. 2, pp. 184–198, 2014.
  7. X. F. Wang and G. Chen, “Pinning control of scale-free dynamical networks,” Physica A: Statistical Mechanics and its Applications, vol. 310, no. 3-4, pp. 521–531, 2002.
  8. H. Su, Z. Rong, M. Z. Chen, X. Wang, G. Chen, and H. Wang, “Decentralized adaptive pinning control for cluster synchronization of complex dynamical networks,” IEEE Transactions on Cybernetics, vol. 43, no. 1, pp. 394–399, 2012.
  9. X. Li, X. Wang, and G. Chen, “Pinning a complex dynamical network to its equilibrium,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 51, no. 10, pp. 2074–2087, 2004.
  10. W. Lu, X. Li, and Z. Rong, “Global stabilization of complex networks with digraph topologies via a local pinning algorithm,” Automatica, vol. 46, no. 1, pp. 116–121, 2010.
  11. M. Zhan, J. Gao, Y. Wu, and J. Xiao, “Chaos synchronization in coupled systems by applying pinning control,” Physical Review E, vol. 76, no. 3, p. 036203, 2007.
  12. M. Porfiri and M. Di Bernardo, “Criteria for global pinning-controllability of complex networks,” Automatica, vol. 44, no. 12, pp. 3100–3106, 2008.
  13. Q. Song and J. Cao, “On pinning synchronization of directed and undirected complex dynamical networks,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 57, no. 3, pp. 672–680, 2009.
  14. D. Liuzza and P. De Lellis, “Pinning control of higher order nonlinear network systems,” IEEE Control Systems Letters, vol. 5, no. 4, pp. 1225–1230, 2020.
  15. F. Della Rossa, C. J. Vega, and P. De Lellis, “Nonlinear pinning control of stochastic network systems,” Automatica, vol. 147, p. 110712, 2023.
  16. J. M. Montenbruck, M. Bürger, and F. Allgöwer, “Practical synchronization with diffusive couplings,” Automatica, vol. 53, pp. 235–243, 2015.
  17. M. V. Srighakollapu, R. K. Kalaimani, and R. Pasumarthy, “Optimizing driver nodes for structural controllability of temporal networks,” IEEE Transactions on Control of Network Systems, vol. 9, no. 1, pp. 380–389, 2022.
  18. N. Masuda, K. Klemm, and V. M. Eguíluz, “Temporal networks: slowing down diffusion by long lasting interactions,” Physical Review Letters, vol. 111, no. 18, p. 188701, 2013.
  19. D. Ghosh, M. Frasca, A. Rizzo, S. Majhi, S. Rakshit, K. Alfaro-Bittner, and S. Boccaletti, “The synchronized dynamics of time-varying networks,” Physics Reports, vol. 949, pp. 1–63, 2022.
  20. S. Jafarizadeh, “Pinning control of dynamical networks with optimal convergence rate,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 52, no. 11, pp. 7160–7172, 2022.
  21. P. DeLellis, F. Garofalo, and F. L. Iudice, “The partial pinning control strategy for large complex networks,” Automatica, vol. 89, pp. 111–116, 2018.
  22. F. L. Iudice, F. Garofalo, and P. De Lellis, “Bounded partial pinning control of network dynamical systems,” IEEE Transactions on Control of Network Systems, 2022.
  23. X. Zhou, L. Li, and X.-W. Zhao, “Pinning synchronization of delayed complex networks under self-triggered control,” Journal of the Franklin Institute, vol. 358, no. 2, pp. 1599–1618, 2021.
  24. X. Yang, X. Wan, C. Zunshui, J. Cao, Y. Liu, and L. Rutkowski, “Synchronization of switched discrete-time neural networks via quantized output control with actuator fault,” IEEE Transactions on Neural Networks and Learning Systems, vol. 32, no. 9, pp. 4191–4201, 2020.
  25. M. Wang, X. Lu, Q. Yang, Z. Ma, J. Cheng, and K. Li, “Pinning control of successive lag synchronization on a dynamical network with noise perturbation,” Physica A: Statistical Mechanics and its Applications, vol. 593, p. 126899, 2022.
  26. T. Chen, W. Lu, and X. Liu, “Finite time convergence of pinning synchronization with a single nonlinear controller,” Neural Networks, vol. 143, pp. 246–249, 2021.
  27. X. Yu and O. Kaynak, “Sliding mode control made smarter: A computational intelligence perspective,” IEEE Systems, Man, and Cybernetics Magazine, vol. 3, no. 2, pp. 31–34, 2017.
  28. C. Edwards and S. Spurgeon, Sliding mode control: theory and applications. Crc Press, 1998.
  29. Springer, 2014.
  30. X. Liu and T. Chen, “Boundedness and synchronization of y-coupled lorenz systems with or without controllers,” Physica D: Nonlinear Phenomena, vol. 237, no. 5, pp. 630–639, 2008.
  31. P. DeLellis, F. Garofalo, et al., “Novel decentralized adaptive strategies for the synchronization of complex networks,” Automatica, vol. 45, no. 5, pp. 1312–1318, 2009.
  32. P. DeLellis, M. di Bernardo, and G. Russo, “On quad, lipschitz, and contracting vector fields for consensus and synchronization of networks,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 58, no. 3, pp. 576–583, 2010.
  33. R. K. Iyer and J. A. Bilmes, “Submodular optimization with submodular cover and submodular knapsack constraints,” Advances in neural information processing systems, vol. 26, 2013.
  34. M. R. Padmanabhan, Y. Zhu, S. Basu, and A. Pavan, “Maximizing submodular functions under submodular constraints,” in Uncertainty in Artificial Intelligence, pp. 1618–1627, PMLR, 2023.
  35. R. Iyer, S. Jegelka, and J. Bilmes, “Fast semidifferential-based submodular function optimization,” in International Conference on Machine Learning, pp. 855–863, PMLR, 2013.

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now