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Many biomedical engineering fields are studied by combining with nonlinear science which has major advances in theoretical curing related diseases. The coronary artery system is chosen as a muscular blood vessel model. With the change of vessel diameter, some chaotic behaviors will occur which may cause complex diseases such as myocardial infarction.#br#In order to avoid the undesired chaotic motion, this paper investigates the finite-time chaos synchronization problem for a coronary artery system by utilizting high-order sliding mode adaptive control method. First, the error chaos synchronization system is obtained using the master and slave systems. Second, the error chaos synchronization system can be transformed into an integrator chain system by coordinate transformation, which is equivalent to an error chaos synchronization system. Considering that the sliding mode control has main obstacle (the control high activity and chattering phenomenon), a high-order sliding mode adaptive controller is designed for a coronary artery system with unknown disturbances at geometric homogeneity and integral sliding mode surface. The proposed method shows that the drive and response systems are synchronized and the states of the response system track the states of the drive system in finite-time. This approach does not require any information about the bound of disturbances in advance. Theoretic analysis based on Lyapunov theory proves that the systems with the proposed controller could be stabilized in finite-time. The convergence time of the system states is estimated. In order to alleviate the chattering effect, we use tanh(·) function in place of sign(·) function to design an improved high-order sliding mode adaptive controller. Simulation results show that the proposed adaptive sliding mode controller can achieve better robustness and adaptation against disturbances, which offer the theoretic basis for curing myocardial infarction.
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Keywords:
- coronary artery system /
- chaos synchronization /
- high-order sliding mode control /
- geometric homogeneity
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[24] Yin S, Li X W, Gao H J, Kaynak O 2015 IEEE Trans. Ind. Electron. 62 657
[25] Yin S, Zhu X P, Kaynak O 2015 IEEE Trans. Ind. Electron. 62 1651
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[1] Guan J B 2010 Chin. Phys. Lett. 27 20502
[2] Magrans R, Gomis P, Caminal P 2013 Med. Eng. Phys. 35 1070
[3] Liu X, Ma B W, Liu H J 2013 Acta Phys. Sin. 62 020202 (in Chinese) [刘仙, 马百旺, 刘会军. 2013 62 020202]
[4] Gu Y F, Xiao J 2014 Acta Phys. Sin. 62 160506 [古元凤, 肖剑 2014 62 160506]
[5] Li W 2012 Int J. Syst Sci. 43 21
[6] Lin C J, Yang S K, Yau H T 2012 Comput. Math. Appl. 64 988
[7] Wang T, Gao H J, Qiu J 2015 IEEE Trans. Neur. Net. Lear.24 11671
[8] Li H Y, Wu C W, Shi P, Gao Y B 2015 IEEE Trans. Cybern. (In press) DOI: 10.1109/TCYB 2014.2371814
[9] Li H Y, Wu C W, Wu, L G, Lam H K 2015 IEEE Trans. Cybern. (In press) DOI 10.1109/TCYB 2015.2413134
[10] Li H Y, Sun X J, Shi P, Lam H K 2015 Inform. Sciences 302 1
[11] Xiu C B, Liu C, Guo F H, Cheng Y, Luo J 2015 Acta Phys. Sin. 64 060504 (in Chinese) [修春波, 刘畅, 郭富慧, 成怡, 罗菁 2015 64 060504]
[12] Gao H J, Chen T W, Lam J 2008 Automatica 44 39
[13] Li H Y, Jing X J, Karimi H R 2014 IEEE Trans. Ind. Electron. 61 436
[14] Li H Y, Yu J, Hilton C, Liu H 2013 IEEE Trans. Ind. Electron. 60 3328
[15] Fridman L, Davila J., Levant A 2011 Nonlinear Anal. 5 189
[16] Laghrouche S, Plestan F, Glumineau A 2007 Automatica43 531
[17] Defoort M, Floquet T, Kokosy A 2009 Syst. Control Lett. 58 102
[18] Gabriela A, Hernández G, Fridman L 2013 C ontrol Eng. Pract. 21 747
[19] Gong C Y, Li Y M, Sun X H 2007 J. Biomath.22 503 (in Chinese) [贡崇颖, 李医民, 孙曦浩 2007 生物数学学报 22 503]
[20] Levant A 2001 IEEE T. Automat. Contr. 49 1447
[21] Bhat S, Bernstein D 2005 Math Control Signal17 101
[22] Bhat S, Bernstein D 2000 SIAM J. Control Optim. 38 751
[23] Yin S, Ding S X, Xie X C, Luo H 2014 IEEE Trans. Ind. Electron. 61 6418
[24] Yin S, Li X W, Gao H J, Kaynak O 2015 IEEE Trans. Ind. Electron. 62 657
[25] Yin S, Zhu X P, Kaynak O 2015 IEEE Trans. Ind. Electron. 62 1651
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