Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Neural Inverse Optimal Pinning Control of Output Trajectory Tracking for Uncertain Complex Networks with Nonidentical Nodes

  • Chapter
  • First Online:
Hybrid Intelligent Systems in Control, Pattern Recognition and Medicine

Part of the book series: Studies in Computational Intelligence ((SCI,volume 827))

Abstract

This chapter presents the development of a control scheme, we named as neural inverse optimal pinning control to achieve output trajectory tracking on uncertain complex networks with nonidentical nodes. A recurrent high order neural network is used to identify the unknown system dynamics of a small fraction of nodes (pinned ones) and by means of this neural model, an inverse optimal controller is designed to synchronize the whole network at an output desired reference. The proposed controller effectiveness is illustrated via simulations. The illustrative example is composed of a network of ten different chaotic nodes.

This work is supported by CONACYT, Mexico, Project 257200.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. A.Y. Alanis, E.N. Sanchez, A.G. Loukianov, M.A. Perez, Real-time recurrent neural state estimation. IEEE Trans. Neural Netw. 22(3), 497–505 (2011)

    Article  Google Scholar 

  2. A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, C. Zhou, Synchronization in complex networks. Phys. Rep. 469(3), 93–153 (2008)

    Article  MathSciNet  Google Scholar 

  3. A.L. Barabási, R. Albert, Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)

    Article  MathSciNet  Google Scholar 

  4. M. Barahona, L.M. Pecora, Synchronization in small-world systems. Phys. Rev. Lett. 89(5), 054101 (2002)

    Article  Google Scholar 

  5. F. Blaabjerg, R. Teodorescu, M. Liserre, A.V. Timbus, Overview of control and grid synchronization for distributed power generation systems. IEEE Trans. Ind. Electron. 53(5), 1398–1409 (2006)

    Article  Google Scholar 

  6. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.U. Hwang, Complex networks: structure and dynamics. Phys. Rep. 424(4), 175–308 (2006)

    Article  MathSciNet  Google Scholar 

  7. C.P. Chen, G.X. Wen, Y.J. Liu, F.Y. Wang, Adaptive consensus control for a class of nonlinear multiagent time-delay systems using neural networks. IEEE Trans. Neural Netw. Learn. Syst. 25(6), 1217–1226 (2014)

    Article  Google Scholar 

  8. G. Chen, Pinning control and controllability of complex dynamical networks. Int. J. Autom. Comput. 14(1), 1–9 (2017)

    Article  Google Scholar 

  9. G. Chen, T. Ueta, Yet another chaotic attractor. Int. J. Bifurcat. Chaos 9(7), 1465–1466 (1999)

    Article  MathSciNet  Google Scholar 

  10. P. Kokotović, M. Arcak, Constructive nonlinear control: a historical perspective. Automatica 37(5), 637–662 (2001)

    Article  MathSciNet  Google Scholar 

  11. E.B. Kosmatopoulos, M.A. Christodoulou, P.A. Ioannou, Dynamical neural networks that ensure exponential identification error convergence. Neural Netw. 10(2), 299–314 (1997)

    Article  Google Scholar 

  12. E.B. Kosmatopoulos, M.M. Polycarpou, M.A. Christodoulou, P.A. Ioannou, High-order neural network structures for identification of dynamical systems. IEEE Trans. Neural Netw. 6(2), 422–431 (1995)

    Article  Google Scholar 

  13. M. Krstic, H. Deng, Stabilization of nonlinear uncertain systems (Springer, New York, 1998)

    MATH  Google Scholar 

  14. M. Krstic, I. Kanellakopoulos, P.V. Kokotovic et al., Nonlinear and Adaptive Control Design, vol. 222 (Wiley, New York, 1995)

    MATH  Google Scholar 

  15. M. Krstic, Z.H. Li, Inverse optimal design of input-to-state stabilizing nonlinear controllers. IEEE Trans. Autom. Control 43(3), 336–350 (1998)

    Article  MathSciNet  Google Scholar 

  16. A.U. Levin, K.S. Narendra, Control of nonlinear dynamical systems using neural networks. II. Observability, identification, and control. IEEE Trans. Neural Netw. 7(1), 30–42 (1996)

    Article  Google Scholar 

  17. X. Li, X. Wang, G. Chen, Pinning a complex dynamical network to its equilibrium. IEEE Trans. Circ. Syst. I Regul. Pap. 51(10), 2074–2087 (2004)

    Article  MathSciNet  Google Scholar 

  18. Y.Y. Liu, J.J. Slotine, A.L. Barabási, Controllability of complex networks. Nature 473(7346), 167 (2011)

    Article  Google Scholar 

  19. E.N. Lorenz, Deterministic nonperiodic flow. J. Atmos. Sci. 20(2), 130–141 (1963)

    Article  MathSciNet  Google Scholar 

  20. T. Matsumoto, A chaotic attractor from Chua’s circuit. IEEE Trans. Circ. Syst. 31(12), 1055–1058 (1984)

    Article  MathSciNet  Google Scholar 

  21. K.S. Narendra, S. Mukhopadhyay, Adaptive control using neural networks and approximate models. IEEE Trans. Neural Netw. 8(3), 475–485 (1997)

    Article  Google Scholar 

  22. M.E. Newman, The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003)

    Article  MathSciNet  Google Scholar 

  23. L.M. Pecora, T.L. Carroll, Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821 (1990)

    Article  MathSciNet  Google Scholar 

  24. A.S. Poznyak, W. Yu, E.N. Sanchez, J.P. Perez, Nonlinear adaptive trajectory tracking using dynamic neural networks. IEEE Trans. Neural Netw. 10(6), 1402–1411 (1999)

    Article  Google Scholar 

  25. L.J. Ricalde, E.N. Sanchez, Output tracking with constrained inputs via inverse optimal adaptive recurrent neural control. Eng. Appl. Artif. Intell. 21(4), 591–603 (2008)

    Article  Google Scholar 

  26. O.E. Rössler, An equation for continuous chaos. Phys. Lett. A 57(5), 397–398 (1976)

    Article  Google Scholar 

  27. G.A. Rovithakis, M.A. Christodoulou, Adaptive Control with Recurrent High-Order Neural Networks: Theory and Industrial Applications (Springer Science & Business Media, 2012)

    Google Scholar 

  28. E.N. Sanchez, F. Ornelas-Tellez, Discrete-Time Inverse Optimal Control for Nonlinear Systems (CRC Press, Boca Raton, 2017)

    Book  Google Scholar 

  29. E.N. Sanchez, L.J. Ricalde, Chaos control and synchronization, with input saturation, via recurrent neural networks. Neural Netw. 16(5), 711–717 (2003)

    Article  Google Scholar 

  30. E.N. Sanchez, L.J. Ricalde, R. Langari, D. Shahmirzadi, Rollover prediction and control in heavy vehicles via recurrent high order neural networks. Intell. Autom. Soft Comput. 17(1), 95–107 (2011)

    Article  Google Scholar 

  31. E.N. Sanchez, D.I. Rodriguez-Castellanos, G. Chen, R. Ruiz-Cruz, Pinning control of complex network synchronization: a recurrent neural network approach. Int. J. Control Autom. Syst. 1–10 (2017)

    Google Scholar 

  32. R. Sepulchre, M. Jankovic, P.V. Kokotovic, Constructive Nonlinear Control (Springer Science & Business Media, 2012)

    Google Scholar 

  33. F. Sorrentino, M. di Bernardo, F. Garofalo, G. Chen, Controllability of complex networks via pinning. Phys. Rev. E 75(4), 046103 (2007)

    Article  Google Scholar 

  34. J.A. Suykens, J.P. Vandewalle, B.L. de Moor, Artificial Neural Networks for Modelling and Control of Non-linear Systems (Springer Science & Business Media, 2012)

    Google Scholar 

  35. C.J. Vega, E.N. Sanchez, Neural inverse optimal pinning control for synchronization of complex networks with nonidentical chaotic nodes, in 2018 International Joint Conference on Neural Networks (IJCNN) (IEEE, 2018), pp. 1–5

    Google Scholar 

  36. L. Wang, Y.X. Sun, Robustness of pinning a general complex dynamical network. Phys. Lett. A 374(15–16), 1699–1703 (2010)

    Article  Google Scholar 

  37. X.F. Wang, G. Chen, Pinning control of scale-free dynamical networks. Phys. A Stat. Mech. Appl. 310(3), 521–531 (2002)

    Article  MathSciNet  Google Scholar 

  38. X.F. Wang, G. Chen, Complex networks: small-world, scale-free and beyond. IEEE Circ. Syst. Mag. 3(1), 6–20 (2003)

    Article  MathSciNet  Google Scholar 

  39. D.J. Watts, S.H. Strogatz, Collective dynamics of small-world networks. Nature 393(6684), 440–442 (1998)

    Article  Google Scholar 

  40. J. Xiang, G. Chen, On the v-stability of complex dynamical networks. Automatica 43(6), 1049–1057 (2007)

    Article  MathSciNet  Google Scholar 

  41. J. Xiang, G. Chen, Analysis of pinning-controlled networks: a renormalization approach. IEEE Trans. Autom. Control 54(8), 1869–1875 (2009)

    Article  MathSciNet  Google Scholar 

  42. L. Xiang, Z. Chen, Z. Liu, F. Chen, Z. Yuan, Pinning control of complex dynamical networks with heterogeneous delays. Comput. Math. Appl. 56(5), 1423–1433 (2008)

    Article  MathSciNet  Google Scholar 

  43. J. Zhou, T. Chen, Synchronization in general complex delayed dynamical networks. IEEE Trans. Circ. Syst. I Regul. Pap. 53(3), 733–744 (2006)

    Article  MathSciNet  Google Scholar 

  44. J. Zhou, J.S. Lu, J. Lü, Pinning adaptive synchronization of a general complex dynamical network. Automatica 44(4), 996–1003 (2008)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Electrical Engineering Department, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Av. del Bosque 1145, Col. El Bajío, 45019, Zapopan, Jalisco, Mexico

    Carlos J. Vega & Edgar N. Sanchez

Authors
  1. Carlos J. Vega
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Edgar N. Sanchez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Edgar N. Sanchez .

Editor information

Editors and Affiliations

  1. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

  2. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Patricia Melin

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Vega, C.J., Sanchez, E.N. (2020). Neural Inverse Optimal Pinning Control of Output Trajectory Tracking for Uncertain Complex Networks with Nonidentical Nodes. In: Castillo, O., Melin, P. (eds) Hybrid Intelligent Systems in Control, Pattern Recognition and Medicine. Studies in Computational Intelligence, vol 827. Springer, Cham. https://doi.org/10.1007/978-3-030-34135-0_24

Download citation

Publish with us

Policies and ethics

Search

Navigation