Hindawi Publishing Corporation Te Scientifc World Journal Volume 2013, Article ID 467276, 13 pages http://dx.doi.org/10.1155/2013/467276 Research Article Identification of Input Nonlinear Control Autoregressive Systems Using Fractional Signal Processing Approach Naveed Ishtiaq Chaudhary, 1 Muhammad Asif Zahoor Raja, 2 Junaid Ali Khan, 2 and Muhammad Saeed Aslam 3 1 Department of Electronic Engineering, International Islamic University, Islamabad 44000, Pakistan 2 Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock Campus, Attock 43600, Pakistan 3 Pakistan Institute of Engineering and Applied Sciences, Nilore, Islamabad 45650, Pakistan Correspondence should be addressed to Muhammad Asif Zahoor Raja; muhammad.asif@ciit-attock.edu.pk Received 29 March 2013; Accepted 30 May 2013 Academic Editors: M. F. G. Penedo and A. Ruano Copyright © 2013 Naveed Ishtiaq Chaudhary et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A novel algorithm is developed based on fractional signal processing approach for parameter estimation of input nonlinear control autoregressive (INCAR) models. Te design scheme consists of parameterization of INCAR systems to obtain linear-in-parameter models and to use fractional least mean square algorithm (FLMS) for adaptation of unknown parameter vectors. Te performance analyses of the proposed scheme are carried out with third-order Volterra least mean square (VLMS) and kernel least mean square (KLMS) algorithms based on convergence to the true values of INCAR systems. It is found that the proposed FLMS algorithm provides most accurate and convergent results than those of VLMS and KLMS under diferent scenarios and by taking the low-to- high signal-to-noise ratio. 1. Introduction Parameter estimation methods have been applied in many important applications arising in applied science and engi- neering including linear and nonlinear system identifcation, signal processing, and adaptive control [1–9]. Nonlinear systems are generally categorized into input, output, feed- back, and hybrid, that is, combination of input and output nonlinear systems. Many nonlinear systems are modeled with Hammerstein model, a class of input nonlinear systems that consists of static nonlinear blocks followed by linear dynam- ical subsystems [10, 11]. Such models have been broadly used in diverse felds such as nonlinear fltering [12], biological systems [13], actuator saturations [14], chemical processes [15], audiovisual processing [16], and signal analysis [17]. A lot of interest has been shown by the research com- munity for parameter estimation of Hammerstein nonlin- ear controlled autoregression models also known as input nonlinear controlled auto-regression (INCAR) systems. For instance, Ding and Chen have developed a least square based iterative procedure and an adaptive extended version of the least square algorithm for Hammerstein autoregressive mov- ing average with exogenous inputs (ARMAX) system [18], Ding et al. also present an auxiliary model using recursive least square algorithm for Hammerstein output error systems [19], and Fan et al. have developed the least square identif- cation algorithm for Hammerstein nonlinear autoregressive with exogenous inputs (ARX) models, while Wang and Ding have developed the extended stochastic gradient algorithm for Hammerstein-Wiener ARMAX models. As per authors’ literature survey adaptive or recursive algorithms based on fractional signal processing approach like fractional least mean square algorithm (FLMS) and its normalized version have not been exploited in this domain. Te application of fractional signal processing has been arising in many felds of science and technology including modeling of fractional Brownian motion [20], description of fractional damping [21], charge estimation of lead acid bat- tery through identifcation of fractional systems [22], which diferintegration [23], and Identifying a transfer function from a frequency response[24] etc. Fundamental description,