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Fuzzy adaptive unscented Kalman filter control of epileptiform spikes in a class of neural mass models

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Abstract

A new closed-loop control method based on the fuzzy adaptive unscented Kalman filter (FAUKF) is proposed to suppress epileptiform spikes in a class of neural mass models with uncertain measurement noise. The FAUKF is used to estimate the nonlinear system states of the underlying models and amend measurement noise adaptively. The control law is constructed via the estimated states. Numerical simulations illustrate the efficiency of the proposed method.

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References

  1. Wendling, F., Bellanger, J.J., Bartolomei, F., Chauvel, P.: Relevance of nonlinear lumped-parameter models in the analysis of depth-EEG epileptic signals. Biol. Cybern. 83, 367–378 (2000)

    Google Scholar 

  2. Gao, J.B., Hu, J., Tung, W.W.: Entropy measures for biological signal analyses. Nonlinear Dyn. 68, 431–444 (2012)

    Google Scholar 

  3. Ding, L., Hou, C.: Stabilizing control of Hopf bifurcation in the Hodgkin–Huxley model via washout filter with linear control term. Nonlinear Dyn. 60, 131–139 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  4. Goodfellow, M., Schindler, K., Baier, G.: Intermittent spike-wave dynamics in a heterogeneous, spatially extended neural mass model. NeuroImage 55, 920–932 (2011)

    Article  Google Scholar 

  5. Goodfellow, M., Schindler, K., Baier, G.: Self-organised transients in a neural mass model of epileptogenic tissue dynamics. NeuroImage 59, 2644–2660 (2012)

    Article  Google Scholar 

  6. Nevado-Holgado, A.J., Marten, F., Richardson, M.P., Terry, J.R.: Characterising the dynamics of EEG waveforms as the path through parameter space of a neural mass model: application to epilepsy seizure evolution. NeuroImage 59, 2374–2392 (2012)

    Article  Google Scholar 

  7. Krauss, G.L., Koubeissi, M.Z.: Cerebellar and thalamic stimulation treatment for epilepsy. Acta Neurochir. Suppl. 97, 347–356 (2007)

    Google Scholar 

  8. Pollo, C., Villemure, J.G.: Rationale, mechanisms of efficacy, anatomical targets and future prospects of electrical deep brain stimulation for epilepsy. Acta Neurochir. Suppl. 97, 311–320 (2007)

    Article  Google Scholar 

  9. Benabid, A.L.: What the future holds for deep brain stimulation. Expert Rev. Med. Devices 4, 895–903 (2007)

    Article  Google Scholar 

  10. Sunderam, S., Gluckman, B., Reato, D., Bikson, M.: Toward rational design of electrical stimulation strategies for epilepsy control. Epilepsy Behav. 17, 6–22 (2010)

    Article  Google Scholar 

  11. Liu, X., Liu, H.J., Tang, Y.G., Gao, Q.: Fuzzy PID control of epileptiform spikes in a neural mass model. Nonlinear Dyn. 71, 13–23 (2013)

    Article  MathSciNet  Google Scholar 

  12. Kalman, R.E.: A new approach to linear filtering and prediction problems. J. Basic Eng. 82, 35–45 (1960)

    Article  Google Scholar 

  13. Wang, H., Han, Z.Z., Zhang, W., Xie, Q.Y.: Chaotic synchronization and secure communication based on descriptor observer. Nonlinear Dyn. 57, 69–73 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  14. Choi, H.H., Jung, J.W.: Fuzzy speed control with an acceleration observer for a permanent magnet synchronous motor. Nonlinear Dyn. 67, 1717–1727 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  15. Gholami, A., Markazi, A.H.D.: A new adaptive fuzzy sliding mode observer for a class of MIMO nonlinear systems. Nonlinear Dyn. 70, 2095–2105 (2012)

    Article  MathSciNet  Google Scholar 

  16. Chong, M., Postoyan, R., Nesic, D., Kuhlmann, L., Varsavsky, A.: A robust circle criterion observer with application to neural mass models. Automatica 48, 2986–2989 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  17. Mariani, S., Ghisi, A.: Unscented Kalman filtering for nonlinear structural dynamics. Nonlinear Dyn. 49, 131–150 (2007)

    Article  MATH  Google Scholar 

  18. Ali, J., Mirza, M.R.U.B.: Performance comparison among some nonlinear filters for a low cost SINS/GPS integrated solution. Nonlinear Dyn. 61(3), 491–502 (2010)

    Article  MATH  Google Scholar 

  19. Schiff, S.J., Sauer, T.: Kalman filter control of a model of spatiotemporal cortical dynamics. J. Neural Eng. 5, 1–8 (2008)

    Google Scholar 

  20. Liu, X., Gao, Q.: Parameter estimation and control for a neural mass model based on the unscented Kalman filter. Phys. Rev. E 88(4), 042905 (2013)

    Google Scholar 

  21. Liu, X., Gao, Q., Li, X.L.: Control of epileptiform spikes based on nonlinear unscented Kalman filter. Chin. Phys. B. 23, 010202 (2014)

    Google Scholar 

  22. Ren, H.W., Zhao, Y.D.: A kind of fuzzy adaptive Kalman filter and its application on INS/Doppler integrated navigation. Aerosp. Control 29, 3–6 (2011)

    Google Scholar 

  23. Xu, T.L., You, W.H., Cui, P.Y.: Research on INS/GPS integrated navigation system based on fuzzy adaptive Kalman filters. J. Astronaut. 26, 571–575 (2005)

    Google Scholar 

  24. Jwo, D.J., Yang, C.F., Chuang, C.H., Lee, T.Y.: Performance enhancement for ultra-tight GPS/INS integration using a fuzzy adaptive strong tracking unscented Kalman filter. Nonlinear Dyn. 73, 377–395 (2013)

    Article  MathSciNet  Google Scholar 

  25. Jansen, B.H., Rit, V.G.: Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biol. Cybern. 73, 357–366 (1995)

    Article  MATH  Google Scholar 

  26. Ma, Z.X., Liu, Z.Y., Chen, M.: Application of adaptive Kalman filtering based on fuzzy logic to the integrated GPS/INS navigation. Inf. Control 35, 457–461 (2006)

    Google Scholar 

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Acknowledgments

This research was supported by the National Natural Science Foundation of China (61004050, 61273260, 61172095, 51207144), the Specialized Research Fund for the Doctoral Program of Higher Education (20101333110006), and the Humanities and Social Sciences Fund, the Ministry of Education Foundation of China (12YJCZH021).

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Authors and Affiliations

  1. Key Lab of Industrial Computer Control Engineering of Hebei Province, Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004, China

    Xian Liu, Hui-Jun Liu, Ying-Gan Tang & Qing Gao

  2. School of Economics, Renmin University of China, Beijing, 100872, China

    Zhan-Ming Chen

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  1. Xian Liu
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  2. Hui-Jun Liu
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  3. Ying-Gan Tang
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  4. Qing Gao
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  5. Zhan-Ming Chen
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Correspondence to Zhan-Ming Chen.

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Liu, X., Liu, HJ., Tang, YG. et al. Fuzzy adaptive unscented Kalman filter control of epileptiform spikes in a class of neural mass models. Nonlinear Dyn 76, 1291–1299 (2014). https://doi.org/10.1007/s11071-013-1210-3

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  • DOI: https://doi.org/10.1007/s11071-013-1210-3

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