Synchronization-based parameter estimation of fractional-order neural networks

This paper focuses on the parameter estimation problem of fractional-order neural network. By combining the adaptive control and parameter update law, we generalize the synchronization-based identification method that has been reported in several literatures on identifying unknown parameters of integer-order systems. With this method, parameter identification and synchronization can be achieved simultaneously. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.

[1]  Eva Kaslik,et al.  Dynamics of fractional-order neural networks , 2011, The 2011 International Joint Conference on Neural Networks.

[2]  Yi Chai,et al.  Lag projective synchronization in fractional-order chaotic (hyperchaotic) systems , 2011 .

[3]  Debin Huang,et al.  Stabilizing near-nonhyperbolic chaotic systems with applications. , 2004, Physical review letters.

[4]  Zhigang Zeng,et al.  Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks , 2014, Neural Networks.

[5]  Jinde Cao,et al.  Adaptive synchronization of a class of chaotic neural networks with known or unknown parameters , 2008 .

[6]  Jinde Cao,et al.  Parameter identification of dynamical systems from time series. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Jinde Cao,et al.  Adaptive synchronization of fractional-order memristor-based neural networks with time delay , 2015, Nonlinear Dynamics.

[8]  Haijun Jiang,et al.  Projective synchronization for fractional neural networks , 2014, Neural Networks.

[9]  Yongguang Yu,et al.  Mittag-Leffler stability of fractional-order Hopfield neural networks , 2015 .

[10]  V. Lakshmikantham,et al.  Theory of Fractional Dynamic Systems , 2009 .

[11]  A. Fairhall,et al.  Fractional differentiation by neocortical pyramidal neurons , 2008, Nature Neuroscience.

[12]  Yan Pei,et al.  Chaotic Evolution: fusion of chaotic ergodicity and evolutionary iteration for optimization , 2014, Natural Computing.

[13]  Haijun Jiang,et al.  Α-stability and Α-synchronization for Fractional-order Neural Networks , 2012, Neural Networks.

[14]  Weihua Deng,et al.  Remarks on fractional derivatives , 2007, Appl. Math. Comput..

[15]  N. Ford,et al.  A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations , 2013 .

[16]  Wei Zhu,et al.  Function projective synchronization for fractional-order chaotic systems , 2011 .

[17]  Eva Kaslik,et al.  Nonlinear dynamics and chaos in fractional-order neural networks , 2012, Neural Networks.

[18]  Jinde Cao,et al.  Dynamics in fractional-order neural networks , 2014, Neurocomputing.

[19]  Guoguang Wen,et al.  Hybrid projective synchronization of time-delayed fractional order chaotic systems , 2014 .

[20]  Parlitz,et al.  Estimating model parameters from time series by autosynchronization. , 1996, Physical review letters.

[21]  Jinde Cao,et al.  New synchronization criteria for memristor-based networks: Adaptive control and feedback control schemes , 2015, Neural Networks.

[22]  Guoguang Wen,et al.  Stability Analysis of Fractional-Order Neural Networks with Time Delay , 2014, Neural Processing Letters.

[23]  Yaolin Jiang,et al.  Generalized projective synchronization of fractional order chaotic systems , 2008 .

[24]  Haijun Jiang,et al.  Corrigendum to "Projective synchronization for fractional neural networks" , 2015, Neural Networks.

[25]  Junzhi Yu,et al.  Global stability analysis of fractional-order Hopfield neural networks with time delay , 2015, Neurocomputing.

[26]  Ljupco Kocarev,et al.  Estimating topology of networks. , 2006, Physical review letters.

[27]  Guoguang Wen,et al.  Stability analysis of fractional-order Hopfield neural networks with time delays , 2014, Neural Networks.

[28]  Sha Wang,et al.  Hybrid projective synchronization of chaotic fractional order systems with different dimensions , 2010 .

[29]  Debin Huang Synchronization-based estimation of all parameters of chaotic systems from time series. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Yixian Yang,et al.  Conditions of parameter identification from time series. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  R. Konnur Synchronization-based approach for estimating all model parameters of chaotic systems. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Jinde Cao,et al.  Projective synchronization of fractional-order memristor-based neural networks , 2015, Neural Networks.

[33]  Tiedong Ma,et al.  Dynamic analysis of a class of fractional-order neural networks with delay , 2013, Neurocomputing.

[34]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[35]  I. Podlubny Fractional differential equations , 1998 .