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Chin. Phys. B, 2015, Vol. 24(9): 090207    DOI: 10.1088/1674-1056/24/9/090207
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A novel observer design method for neural mass models

Liu Xian (刘仙)a, Miao Dong-Kai (苗东凯)a, Gao Qing (高庆)a, Xu Shi-Yun (徐式蕴)b
a Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Institute of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China;
b China Electric Power Research Institute, Beijing 100192, China
Abstract  

Neural mass models can simulate the generation of electroencephalography (EEG) signals with different rhythms, and therefore the observation of the states of these models plays a significant role in brain research. The structure of neural mass models is special in that they can be expressed as Lurie systems. The developed techniques in Lurie system theory are applicable to these models. We here provide a new observer design method for neural mass models by transforming these models and the corresponding error systems into nonlinear systems with Lurie form. The purpose is to establish appropriate conditions which ensure the convergence of the estimation error. The effectiveness of the proposed method is illustrated by numerical simulations.

Keywords:  observer design      neural mass model      Lurie system theory  
Received:  24 January 2015      Revised:  07 May 2015      Accepted manuscript online: 
PACS:  02.30.Yy (Control theory)  
  87.19.le (EEG and MEG)  
Fund: 

Project supported by the National Natural Science Foundation of China (Grant Nos. 61473245, 61004050, and 51207144).

Corresponding Authors:  Liu Xian     E-mail:  liuxian@ysu.edu.cn

Cite this article: 

Liu Xian (刘仙), Miao Dong-Kai (苗东凯), Gao Qing (高庆), Xu Shi-Yun (徐式蕴) A novel observer design method for neural mass models 2015 Chin. Phys. B 24 090207

[1] Li L, Jin Z L and Li B 2011 Chin. Phys. B 20 038701
[2] Wang J and Zhao D Q 2012 Chin. Phys. B 21 028703
[3] Naro D, Rummel C, Schindler K and Andrzejak R G 2014 Phys. Rev. E 90 032913
[4] Sun J F, Tang Y Y, Lim K O, Wang J J, Tong S B, Li H and He B 2014 IEEE Trans. Biomed. Eng. 61 1756
[5] Schomaker J, Berendse H W, Foncke E M J, van der Werf Y D, van den Heuvel O A, Theeuwes J and Meeter M 2014 Neuropsychologia 62 124
[6] Liu X, Gao Q and Li X L 2014 Chin. Phys. B 23 010202
[7] Jansen B H and Rit V G 1995 Biol. Cybern. 73 357
[8] Lopes da Silva F H, Hoeks A, Smits H and Zetterberg L H 1974 Kybernetik 15 27
[9] Wendling F, Bellanger J J, Bartolomei F and Chauvel P 2000 Biol. Cybern. 83 367
[10] David O and Friston K J 2003 NeuroImage 20 1743
[11] Goodfellow M, Schindler K and Baier G 2012 NeuroImage 59 2644
[12] Zandt B J, Visser S, van Putten M J A M and Haken B T 2014 J. Comput. Neurosci. 37 549
[13] Liu X, Liu H J, Tang Y G and Gao Q 2013 Nonlinear Dyn. 71 13
[14] Liu X, Gao Q, Ma B W, Du J J and Ren W J 2013 J. Appl. Math. 2013 792507
[15] Liu X and Gao Q 2013 Phys. Rev. E 88 042905
[16] Shan B N, Wang J, Deng B, Wei X L, Yu H T and Li H Y 2015 Cogn. Neurodyn. 9 31
[17] Liang H J, Zhang H G, Wang Z S and Wang J Y 2014 Chin. Phys. B 23 018902
[18] Koldychev M and Nielsen C 2014 IEEE Trans. Autom. Control 59 2772
[19] Ge S S and Li Z J 2014 IEEE Trans. Autom. Control 59 1624
[20] Schiff S J 2011 Neural Control Engineering: The Emerging Intersection Between Control Theory and Neuroscience (London: The MIT Press)
[21] Leonov G A, Ponomarenko D V and Smirnova V B 1996 Frequency-Domain Methods for Nonlinear Analysis: Theory and Applications (Singapore: World Scientific)
[22] Boyd S, Ghaoui L E, Feron E and Balakrishnan V 1994 Linear Matrix Inequalities in System and Control Theory (Philadelphia: SIAM)
[23] Arcak M and Kokotović P 2001 Automatica 37 1923
[24] Fan X Z and Arcak M 2003 Systems & Control Letters 50 319
[25] Zemouche A and Boutayeb M 2009 Systems & Control Letters 58 282
[26] Chong M, Postoyan R, Nešić D, Kuhlmann L and Varsavsky A 2012 Automatica 48 2986
[27] Liu X, Miao D K and Gao Q 2014 The Scientific World Journal 2014 215943
[28] Liu X, Wang J Z and Huang L 2007 Physica A 383 733
[29] Liu X, Wang J Z and Huang L 2007 Physica A 386 543
[30] Liu X, Wang J Z, Duan Z S and Huang L 2010 Int. J. Robust Nonlin. 20 659
[31] Liu X, Gao Q and Niu L Y 2010 Nonlinear Dyn. 59 297
[32] Xu S Y, Yang Y, Liu X, Tang Y and Sun H D 2011 Chin. Phys. B 20 020509
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