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Mathematical Problems in Engineering
Volume 2017, Article ID 6832575, 8 pages
https://doi.org/10.1155/2017/6832575
Research Article

The Controller Design of the Epilepsy Therapy Apparatus

Ning Li,1 Haiyi Sun,2 and Qingling Zhang1

1College of Sciences, Northeastern University, Shenyang, China
2College of Science, Shenyang Jianzhu University, Shenyang, China

Correspondence should be addressed to Haiyi Sun; moc.361@xx_yhs

Received 27 June 2017; Revised 2 September 2017; Accepted 13 September 2017; Published 25 October 2017

Academic Editor: Quanxin Zhu

Copyright © 2017 Ning Li 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. P. J. Uhlhaas and W. Singer, “Abnormal neural oscillations and synchrony in schizophrenia,” Nature Reviews Neuroscience, vol. 11, no. 2, pp. 100–113, 2010. View at Publisher · View at Google Scholar · View at Scopus
  2. J. E. Zeber, L. A. Copeland, M. Amuan, J. A. Cramer, and M. J. V. Pugh, “The role of comorbid psychiatric conditions in health status in epilepsy,” Epilepsy & Behavior, vol. 10, no. 4, pp. 539–546, 2007. View at Publisher · View at Google Scholar · View at Scopus
  3. J. Wang, G. S. Yi, H. R. Bian et al., “Accurate close-loop desynchronization control of deep brain stimulation,” Journal of Tianjin University, vol. 46, no. 11, pp. 969–976, 2013. View at Google Scholar · View at MathSciNet
  4. M. L. Kringelbach, N. Jenkinson, S. L. F. Owen, and T. Z. Aziz, “Translational principles of deep brain stimulation,” Nature Reviews Neuroscience, vol. 8, no. 8, pp. 623–635, 2007. View at Publisher · View at Google Scholar · View at Scopus
  5. D. C. Medeiros and M. F. D. Moraes, “Focus on desynchronization rather than excitability: a new strategy for intraencephalic electrical stimulation,” Epilepsy & Behavior, vol. 38, no. 1, pp. 32–36, 2014. View at Publisher · View at Google Scholar · View at Scopus
  6. D. J. Watts and S. H. Strogatz, “Collective dynamics of “small-world” networks,” Nature, vol. 393, no. 6684, pp. 440–442, 1998. View at Publisher · View at Google Scholar · View at Scopus
  7. A.-L. Barabási and R. Albert, “Emergence of scaling in random networks,” American Association for the Advancement of Science: Science, vol. 286, no. 5439, pp. 509–512, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  8. Q. Zhu, J. Cao, and R. Rakkiyappan, “Exponential input-to-state stability of stochastic Cohen-Grossberg neural networks with mixed delays,” Nonlinear Dynamics, vol. 79, no. 2, pp. 1085–1098, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. M. E. Newman, “The structure and function of complex networks,” SIAM Review, vol. 45, no. 2, pp. 167–256, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. T. W. Berger, G. Gerhardt, M. A. Liker, and W. Soussou, “The impact of neurotechnology on rehabilitation.,” IEEE Reviews in Biomedical Engineering, vol. 1, pp. 157–197, 2008. View at Publisher · View at Google Scholar · View at Scopus
  11. D. Zhai, L. An, J. Li, and Q. Zhang, “Fault detection for stochastic parameter-varying Markovian jump systems with application to networked control systems,” Applied Mathematical Modelling: Simulation and Computation for Engineering and Environmental Systems, vol. 40, no. 3, pp. 2368–2383, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. Q. Zhu, “Razumikhin-type theorem for stochastic functional differential equations with Lévy noise and Markov switching,” International Journal of Control, vol. 90, no. 8, pp. 1703–1712, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  13. C. Hauptmann, O. Popovych, and P. A. Tass, “Demand-controlled desynchronization of oscillatory networks by means of a multisite delayed feedback stimulation,” Computing and Visualization in Science, vol. 10, no. 2, pp. 71–78, 2007. View at Publisher · View at Google Scholar · View at Scopus
  14. W. Yu, J. Cao, and W. Lu, “Synchronization control of switched linearly coupled neural networks with delay,” Neurocomputing, vol. 73, no. 4–6, pp. 858–866, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. H. Bao, J. H. Park, and J. Cao, “Matrix measure strategies for exponential synchronization and anti-synchronization of memristor-based neural networks with time-varying delays,” Applied Mathematics and Computation, vol. 270, Article ID 21588, pp. 543–556, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. R. Rakkiyappan, V. Preethi Latha, Q. Zhu, and Z. Yao, “Exponential synchronization of Markovian jumping chaotic neural networks with sampled-data and saturating actuators,” Nonlinear Analysis: Hybrid Systems, vol. 24, pp. 28–44, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. X. Yang, J. Cao, Y. Long, and W. Rui, “Adaptive lag synchronization for competive neural networks with mixed delays and uncertain hybrid perturbations,” IEEE Transactions on Neural Networks and Learning Systems, vol. 21, no. 10, pp. 1656–1667, 2010. View at Publisher · View at Google Scholar · View at Scopus
  18. Z. Tu, N. Ding, L. Li et al., “Adaptive synchronization of memristive neural networks with time-varying delays and reaction–diffusion term,” Applied Mathematics & Computation, vol. 311, pp. 118–128, 2017. View at Google Scholar
  19. B. Wang and Q. X. Zhu, “Stability analysis of Markov switched stochastic differential equations with both stable and unstable subsystems,” Systems & Control Letters, vol. 105, pp. 55–61, 2017. View at Google Scholar · View at MathSciNet
  20. Q. X. Zhu and Q. Y. Zhang, “pth moment exponential stabilisation of hybrid stochastic differential equations by feedback controls based on discrete-time state observations with a time delay,” IET Control Theory & Applications, vol. 11, no. 12, pp. 1992–2003, 2017. View at Google Scholar
  21. X. Liu, K. Zhang, and W. C. Xie, “Pinning impulsive synchronization of reaction-diffusion neural networks with time-varying delays,” IEEE Transactions on Neural Networks & Learning Systems, vol. 28, no. 5, pp. 1055–1067, 2016. View at Google Scholar
  22. W. He, F. Qian, and J. Cao, “Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control,” Neural Networks, vol. 85, pp. 1–9, 2017. View at Publisher · View at Google Scholar · View at Scopus
  23. J.-L. Wang, H.-N. Wu, T. Huang, S.-Y. Ren, and J. Wu, “Pinning control for synchronization of coupled reaction-diffusion neural networks with directed topologies,” IEEE Transactions on Systems Man & Cybernetics Systems, vol. 46, no. 8, pp. 1109–1120, 2016. View at Publisher · View at Google Scholar · View at Scopus
  24. M. A. A. Ahmed, Y. Liu, W. Zhang, and F. E. Alsaadi, “Exponential synchronization via pinning adaptive control for complex networks of networks with time delays,” Neurocomputing, vol. 225, pp. 198–204, 2017. View at Publisher · View at Google Scholar · View at Scopus
  25. Y. Ma and Y. Zheng, “Projective lag synchronization of Markovian jumping neural networks with mode-dependent mixed time-delays based on an integral sliding mode controller,” Neurocomputing, vol. 168, pp. 626–636, 2015. View at Publisher · View at Google Scholar · View at Scopus
  26. G. Velmurugan, R. Rakkiyappan, and J. Cao, “Finite-time synchronization of fractional-order memristor-based neural networks with time delays,” Neural Networks, vol. 73, pp. 36–46, 2016. View at Publisher · View at Google Scholar · View at Scopus
  27. Y. Wu, J. Cao, Q. Li, A. Alsaedi, and F. E. Alsaadi, “Finite-time synchronization of uncertain coupled switched neural networks under asynchronous switching,” Neural Networks, vol. 85, pp. 128–139, 2017. View at Publisher · View at Google Scholar · View at Scopus
  28. H. Wang and Q. Zhu, “Finite-time stabilization of high-order stochastic nonlinear systems in strict-feedback form,” Automatica, vol. 54, pp. 284–291, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. A. Khanzadeh and M. Pourgholi, “Fixed-time sliding mode controller design for synchronization of complex dynamical networks,” Nonlinear Dynamics, vol. 88, no. 4, pp. 2637–2649, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. N. Li, H. Sun, X. Jing, and Q. Zhang, “Exponential synchronisation of united complex dynamical networks with multi-links via adaptive periodically intermittent control,” IET Control Theory & Applications, vol. 7, no. 13, pp. 1725–1736, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. L. Zhang, Y. Yang, and F. wang, “Lag synchronization for fractional-order memristive neural networks via period intermittent control,” Nonlinear Dynamics, vol. 89, no. 1, pp. 367–381, 2017. View at Publisher · View at Google Scholar · View at Scopus
  32. M. A. Cohen and S. Grossberg, “Absolute Stability of Global Pattern Formation and Parallel Memory Storage by Competitive Neural Networks,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 13, no. 5, pp. 815–826, 1983. View at Publisher · View at Google Scholar · View at Scopus
  33. K. Gu and S.-I. Niculescu, “Further remarks on additional dynamics in various model transformations of linear delay systems,” Institute of Electrical and Electronics Engineers Transactions on Automatic Control, vol. 46, no. 3, pp. 497–500, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus