Normalized fractional adaptive methods for nonlinear control autoregressive systems

Abstract The trend of applying mathematical foundations of fractional calculus to solve problems arising in nonlinear sciences, is an emerging area of research with growing interest especially in communication, signal analysis and control. In the present study, normalized fractional adaptive strategies are exploited for automatic tuning of the step size parameter in nonlinear system identification based on Hammerstein model. The brilliance of the methodology is verified by mean of viable estimation of electrically stimulated muscle model used in rehabilitation of paralyzed muscles. The dominance of the schemes is established by comparing the results with standard counterparts in case of different noise levels and fractional order variations. The results of the statistical analyses for sufficient independent runs in terms of Nash-Sutcliffe efficiency, variance account for and mean square error metrics validated the consistent accuracy and reliability of the proposed methods. The proposed exploitation of fractional calculus concepts makes a firm branch of nonlinear investigation in arbitrary order gradient-based optimization schemes.

[1]  Yuquan Chen,et al.  An innovative parameter estimation for fractional-order systems in the presence of outliers , 2017 .

[2]  Syed Zubair,et al.  A new computing approach for power signal modeling using fractional adaptive algorithms. , 2017, ISA transactions.

[3]  F. Ding.  Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling , 2013 .

[4]  Raja Muhammad Asif Zahoor,et al.  Bio-inspired computational heuristics for parameter estimation of nonlinear Hammerstein controlled autoregressive system , 2018, Neural Computing and Applications.

[5]  Hari M. Srivastava,et al.  Local fractional similarity solution for the diffusion equation defined on Cantor sets , 2015, Appl. Math. Lett..

[6]  Eric Rogers,et al.  Identification of electrically stimulated muscle models of stroke patients , 2010 .

[7]  Zhiqiang He,et al.  A Novel Generalization of Modified LMS Algorithm to Fractional Order , 2015, IEEE Signal Processing Letters.

[8]  B. Shoaib,et al.  A modified fractional least mean square algorithm for chaotic and nonstationary time series prediction , 2014 .

[9]  Eric A. Butcher,et al.  Numerical solution of multi-order fractional differential equations with multiple delays via spectral collocation methods , 2018 .

[10]  Badr Saad T. Alkahtani,et al.  Analysis of non-homogeneous heat model with new trend of derivative with fractional order , 2016 .

[11]  Eric Rogers,et al.  Recursive identification of Hammerstein systems with application to electrically stimulated muscle , 2012 .

[12]  Feng Ding,et al.  Parameter estimation algorithms for multivariable Hammerstein CARMA systems , 2016, Inf. Sci..

[13]  Raja Muhammad Asif Zahoor,et al.  Novel generalization of Volterra LMS algorithm to fractional order with application to system identification , 2018, Neural Computing and Applications.

[14]  Naveed Ishtiaq Chaudhary,et al.  Design of modified fractional adaptive strategies for Hammerstein nonlinear control autoregressive systems , 2015 .

[15]  Dongqing Wang,et al.  Model recovery for Hammerstein systems using the auxiliary model based orthogonal matching pursuit method , 2018 .

[16]  Songsong Cheng,et al.  A universal modified LMS algorithm with iteration order hybrid switching. , 2017, ISA transactions.

[17]  Allen Q. Ye,et al.  Anisotropic fractional diffusion tensor imaging , 2016, Journal of vibration and control : JVC.

[18]  YangQuan Chen,et al.  Fractional-order exponential switching technique to enhance sliding mode control , 2017 .

[19]  José António Tenreiro Machado,et al.  Integer/fractional decomposition of the impulse response of fractional linear systems , 2015, Signal Process..

[20]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[21]  Robert R. Bitmead,et al.  Closed-Loop Identification of Hammerstein Systems with Application to Gas Turbines , 2014 .

[22]  José António Tenreiro Machado,et al.  Fractional signal processing and applications , 2015, Signal Process..

[23]  M. G. López-López,et al.  Triple pendulum model involving fractional derivatives with different kernels , 2016 .

[24]  Mingyang Pan,et al.  A spatial-fractional thermal transport model for nanofluid in porous media , 2017 .

[25]  Jonathon A. Chambers,et al.  Fractional normalised filtered-error least mean squares algorithm for application in active noise control systems , 2014 .

[26]  F. Mainardi,et al.  Recent history of fractional calculus , 2011 .

[27]  Vladimir Stojanovic,et al.  Adaptive Input Design for Identification of Output Error Model with Constrained Output , 2014, Circuits Syst. Signal Process..

[28]  Raja Muhammad Asif Zahoor,et al.  Design of momentum LMS adaptive strategy for parameter estimation of Hammerstein controlled autoregressive systems , 2016, Neural Computing and Applications.

[29]  Feng Ding,et al.  A novel parameter separation based identification algorithm for Hammerstein systems , 2016, Appl. Math. Lett..

[30]  Vladimir Stojanovic,et al.  Identification of time‐varying OE models in presence of non‐Gaussian noise: Application to pneumatic servo drives , 2016 .

[31]  Hamed Mojallali,et al.  Recursive identification of multiple-input single-output fractional-order Hammerstein model with time delay , 2018, Appl. Soft Comput..

[32]  Vladimir Stojanovic,et al.  Optimal experiment design for identification of ARX models with constrained output in non-Gaussian noise , 2016 .

[33]  Xinggao Liu,et al.  Recursive maximum likelihood method for the identification of Hammerstein ARMAX system , 2016 .

[34]  Raja Muhammad Asif Zahoor,et al.  Design of fractional adaptive strategy for input nonlinear Box-Jenkins systems , 2015, Signal Process..

[35]  H. Salhi,et al.  A recursive parametric estimation algorithm of multivariable nonlinear systems described by Hammerstein mathematical models , 2015 .

[36]  Diyi Chen,et al.  Dynamic characteristics for a hydro-turbine governing system with viscoelastic materials described by fractional calculus , 2017, Applied Mathematical Modelling.

[37]  Raja Muhammad Asif Zahoor,et al.  Modified Volterra LMS algorithm to fractional order for identification of Hammerstein non-linear system , 2017, IET Signal Process..

[38]  Clara Ionescu,et al.  Fractional dynamics and its applications , 2015 .

[39]  Feng Gao,et al.  On a fractal LC-electric circuit modeled by local fractional calculus , 2017, Commun. Nonlinear Sci. Numer. Simul..

[40]  Dumitru Baleanu,et al.  Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis , 2013 .

[41]  Junaid Ali Khan,et al.  Identification of Input Nonlinear Control Autoregressive Systems Using Fractional Signal Processing Approach , 2013, TheScientificWorldJournal.

[42]  José António Tenreiro Machado,et al.  On development of fractional calculus during the last fifty years , 2013, Scientometrics.

[43]  Yi-Fei Pu,et al.  Fractional Extreme Value Adaptive Training Method: Fractional Steepest Descent Approach , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[44]  Naveed Ishtiaq Chaudhary,et al.  Identification of Hammerstein nonlinear ARMAX systems using nonlinear adaptive algorithms , 2015 .

[45]  Behrooz Safarinejadian,et al.  Simultaneous state estimation and parameter identification in linear fractional order systems using coloured measurement noise , 2016, Int. J. Control.

[46]  M. G. Teixeira,et al.  Horizontal water flow in unsaturated porous media using a fractional integral method with an adaptive time step , 2017 .

[47]  Naveed Ishtiaq Chaudhary,et al.  Momentum fractional LMS for power signal parameter estimation , 2018, Signal Process..

[48]  Raja Muhammad Asif Zahoor,et al.  Two-stage fractional least mean square identification algorithm for parameter estimation of CARMA systems , 2015, Signal Process..

[49]  Muhammad Saeed Aslam,et al.  A sliding-window approximation-based fractional adaptive strategy for Hammerstein nonlinear ARMAX systems , 2017 .

[50]  Yigang He,et al.  Generation and circuit implementation of fractional-order multi-scroll attractors , 2016 .

[51]  Mohammad Rostami,et al.  Undamped oscillations in fractional-order Duffing oscillator , 2015, Signal Process..

[52]  Yan Li,et al.  An innovative fractional order LMS based on variable initial value and gradient order , 2017, Signal Process..

[53]  Naveed Ishtiaq Chaudhary,et al.  Design of normalized fractional adaptive algorithms for parameter estimation of control autoregressive autoregressive systems , 2018 .

[54]  YangQuan Chen,et al.  Guest editorial for special issue on fractional order systems and controls , 2016 .

[55]  Sara Dadras,et al.  Performance analysis of fractional order extremum seeking control. , 2016, ISA transactions.

[56]  P. Novati,et al.  The solution of fractional order epidemic model by implicit Adams methods , 2017 .

[57]  Yi-Fei Pu,et al.  A texture image denoising approach based on fractional developmental mathematics , 2015, Pattern Analysis and Applications.

[58]  J. A. Tenreiro Machado,et al.  Special Issue: Advances in Fractional Dynamics and Control , 2016 .

[59]  Masoud Geravanchizadeh,et al.  Speech Enhancement by Modified Convex Combination of Fractional Adaptive Filtering , 2014 .

[60]  António M. Lopes,et al.  A fractional perspective on the trajectory control of redundant and hyper-redundant robot manipulators , 2017 .

[61]  Yong Zhou,et al.  Fractional Evolution Equations and Inclusions: Analysis and Control , 2016 .

[62]  D. Baleanu,et al.  Image encryption technique based on fractional chaotic time series , 2016 .

[63]  I. Turner,et al.  Numerical inversion of the fractional derivative index and surface thermal flux for an anomalous heat conduction model in a multi-layer medium , 2018, Applied Mathematical Modelling.