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In order to remain the structure of the neural network in the process of the optimization unchanged, taking the hysteretic chaotic neuron and the hysteretic chaotic neural network as controlled plants, a novel control strategy based on the filtered tracking error is proposed to perform the stability control for the single hysteretic chaotic neuron or the hysteretic chaotic neural network. Especially, the hysteretic chaotic neuron and the hysteretic chaotic neural network can be used to solve the optimization problem through using the control strategy on condition that the generation mechanisms of the nonlinear characteristics, hysteresis and chaos, are unchanged. The control law is composed of two terms: one is the equivalent control term in the ideal filtered tracking error surface, and the other is the control term which can make the system reach the filtered tracking error surface quickly. Lyapunov stability method is used to prove the stability of the control strategy for the single hysteretic chaotic neuron and hysteretic chaotic neural network. The control laws of hysteretic chaotic neurons can be obtained according to the optimization function. The state of the single hysteretic chaotic neuron or the hysteretic chaotic neural network can converge to an extreme point of the optimization function gradually by the control law. In this way, the optimization problem can be solved effectively. Simulation results prove the feasibility and validity of the control strategy for optimization problem.
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Keywords:
- hysteretic /
- chaos /
- neuron /
- neural network
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[2] Liu X D, Xiu C B 2007 Neurocomputing 70 2561
[3] Xia J W, Park J H, Zeng H B, Shen H 2014 Neurocomputing 140 210
[4] Wang X, Li C D, Huang T W 2014 Neurocomputing 140 155
[5] Lang J, Hao Z C 2014 Opt. Laser Eng. 52 91
[6] Yu S J, Huan R S, Zhang Y, Feng D 2014 Acta Phys. Sin. 63 060701 (in Chinese) [于舒娟, 宦如松, 张昀, 冯迪 2014 63 060701]
[7] Wang X Y, Bao X M 2013 Chin. Phys. B 22 050508
[8] Kalpana M, Balasubramaniam P 2013 Chin. Phys. B 22 078401
[9] Kwon O M, Park M J, Park J H, Lee S M, Cha E J 2013 Chin. Phys. B 22 110504
[10] Zeng Z Z 2013 Acta Phys. Sin. 62 030504 (in Chinese) [曾喆昭 2013 62 030504]
[11] Cao J D, Lu J 2006 Chaos 16 013133
[12] Huang X, Cao J D 2006 Nonlinearity 19 2797
[13] He W L, Cao J D 2009 Nonlinear Dynam. 55 55
[14] Zhu Q X, Cao J D 2010 Nonlinear Dynam. 61 517
[15] Cao J D, Alofi A, Al-Mazrooei A, Elaiw A 2013 Abstr. Appl. Anal. 2013 940573
[16] Liu X D, Xiu C B 2008 Neural Comput. Appl. 17 579
[17] Sun M, Zhao L, Ding J C, Zao X 2010 Syst. Eng. Electron. 32 396 (in Chinese) [孙明, 赵琳, 丁继成, 赵欣 2010 系统工程与电子技术 32 396]
[18] Xiu C B, Liu Y X, Lu L F 2010 Control Eng. China 17 300 (in Chinese) [修春波, 刘玉霞, 陆丽芬 2010 控制工程 17 300]
[19] Yang G, Yi J Y 2014 Neurocomputing 127 114
[20] Ding Z, Leung H, Zhu Z W 2002 Math. Comput. Model. 36 1007
[21] Zhang Q H Y, Xie X P, Zhu P, Chen H P, He G G 2014 Commun. Nonlinear Sci. 19 2793
[22] Li X D, Song S J 2014 Commun. Nonlinear Sci. 19 3892
[23] Zhang X D, Zhu P, Xie X P, He G G 2013 Acta Phys. Sin. 62 210506 (in Chinese) [张旭东, 朱萍, 谢小平, 何国光 2013 62 210506]
[24] Jagannathan S, Vandegrift M W, Lewis F L 2000 Automatica 36 229
[25] Jagannathan S, Lewis F L 2000 Inform. Sci. 123 223
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[1] Bosque G, Campo I D, Echanobe J 2014 Eng. Appl. Artif. Intel. 32 283
[2] Liu X D, Xiu C B 2007 Neurocomputing 70 2561
[3] Xia J W, Park J H, Zeng H B, Shen H 2014 Neurocomputing 140 210
[4] Wang X, Li C D, Huang T W 2014 Neurocomputing 140 155
[5] Lang J, Hao Z C 2014 Opt. Laser Eng. 52 91
[6] Yu S J, Huan R S, Zhang Y, Feng D 2014 Acta Phys. Sin. 63 060701 (in Chinese) [于舒娟, 宦如松, 张昀, 冯迪 2014 63 060701]
[7] Wang X Y, Bao X M 2013 Chin. Phys. B 22 050508
[8] Kalpana M, Balasubramaniam P 2013 Chin. Phys. B 22 078401
[9] Kwon O M, Park M J, Park J H, Lee S M, Cha E J 2013 Chin. Phys. B 22 110504
[10] Zeng Z Z 2013 Acta Phys. Sin. 62 030504 (in Chinese) [曾喆昭 2013 62 030504]
[11] Cao J D, Lu J 2006 Chaos 16 013133
[12] Huang X, Cao J D 2006 Nonlinearity 19 2797
[13] He W L, Cao J D 2009 Nonlinear Dynam. 55 55
[14] Zhu Q X, Cao J D 2010 Nonlinear Dynam. 61 517
[15] Cao J D, Alofi A, Al-Mazrooei A, Elaiw A 2013 Abstr. Appl. Anal. 2013 940573
[16] Liu X D, Xiu C B 2008 Neural Comput. Appl. 17 579
[17] Sun M, Zhao L, Ding J C, Zao X 2010 Syst. Eng. Electron. 32 396 (in Chinese) [孙明, 赵琳, 丁继成, 赵欣 2010 系统工程与电子技术 32 396]
[18] Xiu C B, Liu Y X, Lu L F 2010 Control Eng. China 17 300 (in Chinese) [修春波, 刘玉霞, 陆丽芬 2010 控制工程 17 300]
[19] Yang G, Yi J Y 2014 Neurocomputing 127 114
[20] Ding Z, Leung H, Zhu Z W 2002 Math. Comput. Model. 36 1007
[21] Zhang Q H Y, Xie X P, Zhu P, Chen H P, He G G 2014 Commun. Nonlinear Sci. 19 2793
[22] Li X D, Song S J 2014 Commun. Nonlinear Sci. 19 3892
[23] Zhang X D, Zhu P, Xie X P, He G G 2013 Acta Phys. Sin. 62 210506 (in Chinese) [张旭东, 朱萍, 谢小平, 何国光 2013 62 210506]
[24] Jagannathan S, Vandegrift M W, Lewis F L 2000 Automatica 36 229
[25] Jagannathan S, Lewis F L 2000 Inform. Sci. 123 223
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