Edit Profile (opens in new tab) Billings, Stephen A. Compute Distance To: Compute Author ID: billings.stephen-a Published as: Billings, S. A.; Billings, Stephen A.; Billings, Stephen. A.; Billings, S. more...less Homepage: https://www.sheffield.ac.uk/acse/staff/sab External Links: Wikidata · dblp Documents Indexed: 202 Publications since 1979, including 1 Book 3 Contributions as Editor Co-Authors: 63 Co-Authors with 181 Joint Publications 917 Co-Co-Authors all top 5 Co-Authors 2 single-authored 25 Guo, Lingzhong 24 Coca, Daniel 20 Wei, Hualiang 18 Chen, Sheng 16 Lang, Ziqiang 14 Guo, Yuzhu 10 Jing, Xingjian 10 Tsang, Kai Ming 10 Zhao, Yifan 9 Aguirre, Luis Antonio 9 Zhu, Quanmin 6 Fakhouri, S. Y. 6 Kadirkamanathan, Visakan 6 Owens, David Howard 5 Leontaritis, I. J. 5 Voon, W. S. F. 4 Jones, J. C. Peyton 4 Mao, Kezhi 4 Tomlinson, Geoffrey R. 4 Zinober, Alan Solon Ivor 3 Balikhin, Michael A. 3 El-Ghezawi, O. M. E. 3 Korenberg, Michael J. 3 Mendes, Eduardo M. A. M. 3 Ristic, Rile I. 3 Wu, Xiaofeng 3 Yue, Rong 2 Boaghe, Otilia M. 2 Cowan, Colin F. N. 2 Dematos, L. L. 2 Mei, Shuaishuai 2 Peng, Zhike 2 Routh, Alexander F. 2 Zhang, Bin 1 Alturki, F. A. 1 Anderson, Sean R. 1 Chadwick, M. A. 1 Chang, Hui-Chen 1 Cheng, Shan-Jen 1 Chotai, Arun 1 Clarke, David W. 1 De Matos, Lucy L. 1 Dougherty, Andrew 1 Fung, Patrick Tze-Kwai 1 Gawthrop, Peter J. 1 Gray, John O. 1 Grimble, Michael John 1 Haynes, B. R. 1 He, Fei 1 Jacobs, O. L. R. 1 Jamaluddin, H. B. 1 Jones, G. N. 1 Krishnanathan, Kirubhakaran 1 Kung, I-Chung 1 Lang, Zhiqiang 1 Li, Shaoyuan 1 Linkens, Derek A. 1 Liu, Jui-Jung 1 McIlroy, P. J. 1 Meng, Guang 1 Morris, A. Julian 1 Mort, N. 1 Nazer, L. 1 Parks, P. G. 1 Porth, B. 1 Prager, O. L. 1 Sales, K. R. 1 Sarrigiannis, P. G. 1 Shen, Jianxin 1 Tao, Qinghua 1 Unbehauen, Heinz 1 Wang, Shu 1 Wang, Yongji 1 Wellstead, Peter E. 1 Wood, R. Kevin 1 Wormald, C. N. 1 Yusof, M. I. 1 Zanker, P. M. 1 Zhao, Dongya 1 Zhu, Daqi all top 5 Serials 84 International Journal of Control 35 International Journal of Systems Science 21 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 7 International Journal of Systems Science. Principles and Applications of Systems and Integration 4 Automatica 4 Mechanical Systems and Signal Processing 4 Nonlinear Dynamics 3 Physics Letters. A 3 Systems & Control Letters 3 European Journal of Control 3 IEE Control Engineering Series 3 Journal of Cellular Automata 2 Journal of Sound and Vibration 2 Physica D 2 IMA Journal of Mathematical Control and Information 2 Signal Processing 2 IEE Proceedings. Part D. Control Theory and Applications 1 Journal of Mathematical Analysis and Applications 1 IEEE Transactions on Automatic Control 1 Mathematics and Computers in Simulation 1 Circuits, Systems, and Signal Processing 1 Neural Networks 1 IEEE Transactions on Signal Processing 1 International Journal of Adaptive Control and Signal Processing 1 IEEE Transactions on Circuits and Systems. I: Fundamental Theory and Applications 1 IEEE Transactions on Circuits and Systems. II: Analog and Digital Signal Processing 1 Journal of Nonlinear Science 1 IEE Proceedings. Control Theory and Applications 1 Journal of Vibration and Control 1 Mathematical and Computer Modelling of Dynamical Systems 1 Dynamical Systems 1 Acta Mechanica Sinica 1 IEEE Transactions on Circuits and Systems I: Regular Papers all top 5 Fields 177 Systems theory; control (93-XX) 27 Statistics (62-XX) 24 Dynamical systems and ergodic theory (37-XX) 17 Numerical analysis (65-XX) 14 Biology and other natural sciences (92-XX) 12 Computer science (68-XX) 11 Information and communication theory, circuits (94-XX) 7 Ordinary differential equations (34-XX) 6 Mechanics of particles and systems (70-XX) 5 Partial differential equations (35-XX) 3 General and overarching topics; collections (00-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral equations (45-XX) 2 Operations research, mathematical programming (90-XX) 1 Real functions (26-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Probability theory and stochastic processes (60-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 173 Publications have been cited 1,960 times in 845 Documents Cited by ▼ Year ▼ Orthogonal least squares methods and their application to non-linear system identification. Zbl 0686.93093Chen, S.; Billings, S. A.; Luo, W. 138 1989 Input-output parametric models for non-linear systems. I: deterministic non-linear systems. Zbl 0569.93011Leontaritis, I. J.; Billings, S. A. 124 1985 Representations of nonlinear systems: The NARMAX model. Zbl 0674.93009Chen, S.; Billings, S. A. 77 1989 Nonlinear system identification. NARMAX methods in the time, frequency, and spatio-temporal domains. Zbl 1287.93101Billings, Stephen A. 71 2013 Identification of systems containing linear dynamic and static nonlinear elements. Zbl 0472.93067Billings, S. A.; Fakhouri, S. Y. 62 1982 Orthogonal parameter estimation algorithm for non-linear stochastic systems. Zbl 0647.93062Korenberg, M.; Billings, S. A.; Liu, Y. P.; McIlroy, P. J. 61 1988 Input-output parametric models for nonlinear systems. II: Stochastic nonlinear systems. Zbl 0569.93012Leontaritis, I. J.; Billings, S. A. 53 1985 Non-linear system identification using neural networks. Zbl 0703.93071Chen, Sheng; Billings, S. A.; Grant, P. M. 47 1990 Mapping non-linear integro-differential equations into the frequency domain. Zbl 0721.93041Billings, S. A.; Peyton Jones, J. C. 41 1990 Analysis and design of variable structure systems using a geometric approach. Zbl 0538.93035El-Ghezawi, O. M. E.; Zinober, A. S. I.; Billings, S. A. 39 1983 Recursive algorithm for computing the frequency response of a class of non-linear difference equation models. Zbl 0686.93086Peyton Jones, J. C.; Billings, S. A. 39 1989 Identification of non-linear output-affine systems using an orthogonal least-squares algorithm. Zbl 0669.93015Billings, S. A.; Korenberg, M. J.; Chen, S. 36 1988 A prediction-error and stepwise-regression estimation algorithm for non- linear systems. Zbl 0597.93058Billings, S. A.; Voon, W. S. F. 35 1986 Retrieving dynamical invariants from chaotic data using NARMAX models. Zbl 0886.58100Aguirre, Luis Antonio; Billings, S. A. 32 1995 Neural networks for nonlinear dynamic system modelling and identification. Zbl 0764.93021Chen, S.; Billings, S. A. 31 1992 Output frequency characteristics of nonlinear systems. Zbl 0860.93023Lang, Ziqiang; Billings, S. A. 29 1996 Non-linear system identification using the Hammerstein model. Zbl 0452.93012Billings, S. A.; Fakhouri, S. Y. 27 1979 Nonlinear model validation using correlation tests. Zbl 0813.93012Billings, S. A.; Zhu, Q. M. 24 1994 Dynamical effects of overparametrization in nonlinear models. Zbl 0888.58060Aguirre, Luis Antonio; Billings, S. A. 23 1995 Identification of nonlinear rational systems using a prediction-error estimation algorithm. Zbl 0674.93066Billings, S. A.; Chen, S. 22 1989 Validating identified nonlinear models with chaotic dynamics. Zbl 0876.58028Aguirre, Luis A.; Billings, S. A. 22 1994 Spectral analysis for nonlinear systems. I: Parametric nonlinear spectral analysis. Zbl 0682.93032Billings, S. A.; Tsang, K. M. 21 1989 Practical identification of NARMAX models using radial basis functions. Zbl 0707.93075Chen, Sheng; Billings, S. A.; Cowan, C. F. N.; Grant, P. M. 21 1990 Identification of MIMO nonlinear systems using a forward-regression orthogonal estimator. Zbl 0683.93074Billings, S. A.; Chen, S.; Korenberg, M. J. 21 1989 Output frequency response function of nonlinear Volterra systems. Zbl 1117.93047Lang, Z. Q.; Billings, S. A.; Yue, R.; Li, J. 21 2007 Extended model set, global data and threshold model identification of severely non-linear systems. Zbl 0686.93092Billings, S. A.; Chen, S. 20 1989 Properties of neural networks with application to modelling non-linear dynamical systems. Zbl 0742.93001Billings, S. A.; Jamaluddin, H. B.; Chen, S. 18 1992 Improved structure selection for nonlinear models based on term clustering. Zbl 0837.93009Aguirre, Luis A.; Billings, S. A. 18 1995 Rational model identification using an extended least-squares algorithm. Zbl 0728.93084Billings, S. A.; Zhu, Q. M. 18 1991 Recursive hybrid algorithm for non-linear system identification using radial basis function networks. Zbl 0757.93015Chen, S.; Billings, S. A.; Grant, P. M. 17 1992 Term and variable selection for nonlinear system identification. Zbl 1050.93506Wei, H. L.; Billings, S. A.; Liu, J. 17 2004 Review of rational (total) nonlinear dynamic system modelling, identification, and control. Zbl 1332.93047Zhu, Quanmin; Wang, Yongji; Zhao, Dongya; Li, Shaoyuan; Billings, Stephen A. 16 2015 Identification of coupled map lattice models of complex spatio-temporal patterns. Zbl 0971.37022Coca, D.; Billings, S. A. 16 2001 Algorithms for minimal model structure detection in nonlinear dynamic system identification. Zbl 0889.93017Mao, K. Z.; Billings, S. A. 16 1997 Discrete wavelet models for identification and qualitative analysis of chaotic systems. Zbl 0955.93502Billings, S. A.; Coca, D. 15 1999 Piecewise linear identification of nonlinear systems. Zbl 0615.93070Billings, S. A.; Voon, W. S. F. 15 1987 Model validation tests for multivariable nonlinear models including neural networks. Zbl 0835.93003Billings, S. A.; Zhu, Q. M. 14 1995 Structure detection and model validity tests in the identification of nonlinear systems. Zbl 0513.93053Billings, S. A.; Voon, W. S. F. 14 1983 Spectral analysis for nonlinear systems. II: Interpretation of nonlinear frequency response functions. Zbl 0699.93040Billings, S. A.; Tsang, K. M. 14 1989 Non-linear systems identification using radial basis functions. Zbl 0706.93074Chen, Sheng; Billings, S. A.; Cowan, C. F. N.; Grant, P. M. 14 1990 Correlation based model validity tests for nonlinear models. Zbl 0589.93066Billings, S. A.; Voon, W. S. F. 13 1986 Output frequencies of nonlinear systems. Zbl 0886.93042Lang, Zi-Qiang; Billings, S. A. 13 1997 Effects of the sampling time on the dynamics and identification of nonlinear models. Zbl 0925.93581Billings, S. A.; Aguirre, Luis Antonio 13 1995 Fast orthogonal identification of nonlinear stochastic models and radial basis function neural networks. Zbl 0858.93069Zhu, Q. M.; Billings, S. A. 12 1996 Energy transfer properties of non-linear systems in the frequency domain. Zbl 1088.93012Lang, Z. Q.; Billings, S. A. 12 2005 Fast sampling and stability of nonlinear sampled-data systems. I: Existence theorems. Zbl 0717.93041Owens, D. H.; Zheng, Y.; Billings, S. A. 12 1990 Generalized frequency response function matrix for MIMO nonlinear systems. Zbl 1038.93066Swain, A. K.; Billings, S. A. 12 2001 Continuous-time system identification for linear and nonlinear systems using wavelet decompositions. Zbl 0925.93153Coca, D.; Billings, S. A. 12 1997 The parametric characteristic of frequency response functions for nonlinear systems. Zbl 1125.93048Jing, Xing Jian; Lang, Zi Qiang; Billings, Stephen A.; Tomlinson, Geofrey R. 12 2006 Identification of finite-dimensional models of infinite-dimensional dynamical systems. Zbl 1011.93026Coca, Daniel; Billings, Stephen A. 11 2002 An investigation into the characteristics of nonlinear frequency response functions. I: Understanding the higher dimensional frequency spaces. Zbl 1121.93030Yue, R.; Billings, S. A.; Lang, Z.-Q. 10 2005 Least squares parameter estimation algorithms for non-linear systems. Zbl 0567.93062Billings, S. A.; Voon, W. S. F. 10 1984 Nonlinear system identification using wavelet multiresolution models. Zbl 1024.93061Coca, D.; Billings, S. A. 10 2001 Nonlinear systems in the frequency domain: Energy transfer filters. Zbl 1038.93064Billings, S. A.; Lang, Zi-Qiang 10 2002 Identification of non-linear systems using correlation analysis and pseudorandom inputs. Zbl 0447.93049Billings, S. A.; Fakhouri, S. Y. 9 1980 Identification of models for chaotic systems from noisy data: implications for performance and nonlinear filtering. Zbl 0888.93015Aguirre, Luis Antonio; Billings, S. A. 9 1995 Modelling and analysis of non-linear time series. Zbl 0694.93090Chen, S.; Billings, S. A. 9 1989 Interpolation of nonlinear frequency response functions. Zbl 0708.93035Peyton Jones, J. C.; Billings, S. A. 9 1990 The wavelet-NARMAX representation: a hybrid model structure combining polynomial models with multiresolution wavelet decompositions. Zbl 1068.93004Billings, S. A.; Wei, H. L. 9 2005 Identification and reconstruction of chaotic systems using multiresolution wavelet decompositions. Zbl 1085.93022Wei, H. L.; Billings, S. A. 9 2004 A structure detection algorithm for nonlinear dynamic rational models. Zbl 0825.93762Billings, S. A.; Zhu, Q. M. 9 1994 Generalized multiscale radial basis function networks. Zbl 1254.68197Billings, Stephen A.; Wei, Hua-Liang; Balikhin, Michael A. 8 2007 New bound characteristics of NARX model in the frequency domain. Zbl 1115.93066Jing, X. J.; Lang, Z. Q.; Billings, S. A. 8 2007 Computation of the zeros and zero directions of linear multivariable systems. Zbl 0491.93028El-Ghezawi, O. M. E.; Zinober, A. S. I.; Owens, D. H.; Billings, S. A. 7 1982 Identification of time-varying systems using multiresolution wavelet models. Zbl 1092.93012Wei, Hua-Liang; Billings, S. A. 7 2002 An iterative orthogonal forward regression algorithm. Zbl 1312.93108Guo, Yuzhu; Guo, L. Z.; Billings, S. A.; Wei, Hua-Liang 7 2015 Fast sampling and stability of nonlinear sampled-data systems. II: Sampling rate estimators. Zbl 0717.93042Zheng, Y.; Owens, D. H.; Billings, S. A. 7 1990 Model selection and validation methods for nonlinear systems. Zbl 0617.93069Leontaritis, I. J.; Billings, S. A. 7 1987 Experimental design and identifiability for non-linear systems. Zbl 0619.93066Leontaritis, I. J.; Billings, S. A. 7 1987 Prediction-error estimation algorithm for non-linear output-affine systems. Zbl 0632.93070Chen, S.; Billings, S. A. 7 1988 Model validity tests for non-linear signal processing applications. Zbl 0734.62089Billings, S. A.; Tao, Q. H. 7 1991 Direct parameter identification of distributed parameter systems. Zbl 1080.93531Coca, D.; Billings, S. A. 7 2000 Predictive control for nonlinear systems using neural networks. Zbl 0948.90053Liu, G. P.; Kadirkamanathan, V.; Billings, S. A. 7 1998 Parameter estimation for stochastic nonlinear rational models. Zbl 0782.62084Zhu, Q. M.; Billings, S. A. 6 1993 Frequency response functions for nonlinear rational models. Zbl 0828.93041Zhang, H.; Billings, S. A.; Zhu, Q. M. 6 1995 A bound for the magnitude characteristics of nonlinear ouput frequency response functions. I: Analysis and computation. Zbl 0870.93031Billings, S. A.; Lang, Zi-Qiang 6 1996 Evaluation of output frequency responses of nonlinear systems under multiple inputs. Zbl 0980.93050Lang, Zi-Qiang; Billings, S. A. 6 2000 Self-tuning control of non-linear ARMAX models. Zbl 0708.93089Sales, K. R.; Billings, S. A. 6 1990 Continuous time nonlinear system identification in the frequency domain. Zbl 1010.93030Li, L. M.; Billings, S. A. 6 2001 Givens rotation based fast backward elimination algorithm for RBF neural network pruning. Zbl 0885.93025Hong, X.; Billings, S. A. 6 1997 Frequency domain analysis for non-linear Volterra systems with a general non-linear output function. Zbl 1152.93428Jing, X. J.; Lang, Z. Q.; Billings, S. A. 6 2008 An adaptive orthogonal search algorithm for model subset selection and non-linear system identification. Zbl 1152.93343Billings, S. A.; Wei, H. L. 6 2008 Gain bounds of higher-order nonlinear transfer functions. Zbl 0860.93013Zhang, H.; Billings, S. A. 5 1996 A unified wavelet-based modelling framework for nonlinear system identification: the WANARX model structure. Zbl 1143.93312Wei, H. L.; Billings, S. A. 5 2004 Computational system identification of continuous-time nonlinear systems using approximate Bayesian computation. Zbl 1346.93389Krishnanathan, Kirubhakaran; Anderson, Sean R.; Billings, Stephen A.; Kadirkamanathan, Visakan 5 2016 Self-tuning and adaptive control: theory and applications. Zbl 0497.00019 5 1981 Variable-structure systems and system zeros. Zbl 0527.93020El-Ghezawi, O. M. E.; Billings, S. A.; Zinober, A. S. I. 5 1983 Neural network-based variable structure control for nonlinear discrete systems. Zbl 1015.93504Liu, G. P.; Kadirkamanathan, V.; Billings, S. A. 5 1999 Identification of non-linear \(S_m\) systems. Zbl 0422.93095Billings, S. A.; Fakhouri, S. Y. 5 1979 Multi-directional model validity tests for nonlinear system identification. Zbl 1028.93029Mao, K. Z.; Billings, S. A. 5 2000 Discrete reconstruction of strange attractors of Chua’s circuit. Zbl 0900.70335Aguirre, Luis A.; Billings, S. A. 5 1994 Time series prediction using support vector machines, the orthogonal and the regularized orthogonal least-squares algorithms. Zbl 1013.93055Lee, K. L.; Billings, S. A. 5 2002 Mapping from parametric characteristics to generalized frequency response functions of non-linear systems. Zbl 1152.93429Jing, Xing Jian; Lang, Zi Qiang; Billings, Stephen A. 5 2008 Subharmonic oscillation modeling and MISO Volterra series. Zbl 1368.94174Boaghe, Otilia M.; Billings, Stephen A. 5 2003 Volterra series approximation of a class of nonlinear dynamical systems using the Adomian decomposition method. Zbl 1281.37027Guo, Yuzhu; Guo, L. Z.; Billings, S. A.; Coca, Daniel; Lang, Z. Q. 5 2013 Decomposition of generalized frequency response functions for nonlinear systems using symbolic computation. Zbl 0870.93033Billings, S. A.; Yusof, M. I. 4 1996 Identification of coupled map lattice models of stochastic spatio-temporal dynamics using wavelets. Zbl 1072.93028Guo, L. Z.; Billings, S. A. 4 2004 On overparametrization of nonlinear discrete systems. Zbl 0933.37055Mendes, Eduardo M. A. M.; Billings, S. A. 4 1998 Identification and analysis of spatio-temporal dynamical systems using wavelets. Zbl 1168.93332Guo, L. Z.; Billings, S. A. 4 2008 Nonlinear system identification using wavelet networks. Zbl 1080.93577Liu, G. P.; Billings, S. A.; Kadirkamanathan, V. 4 2000 Computational system identification of continuous-time nonlinear systems using approximate Bayesian computation. Zbl 1346.93389Krishnanathan, Kirubhakaran; Anderson, Sean R.; Billings, Stephen A.; Kadirkamanathan, Visakan 5 2016 Identification of nonlinear time-varying systems using an online sliding-window and common model structure selection (CMSS) approach with applications to EEG. Zbl 1345.93160Li, Yang; Wei, Hua-Liang; Billings, Stephen. A.; Sarrigiannis, P. G. 1 2016 Identification of continuous-time models for nonlinear dynamic systems from discrete data. Zbl 1347.93263Guo, Yuzhu; Guo, Ling Zhong; Billings, Stephen A.; Wei, Hua-Liang 1 2016 Review of rational (total) nonlinear dynamic system modelling, identification, and control. Zbl 1332.93047Zhu, Quanmin; Wang, Yongji; Zhao, Dongya; Li, Shaoyuan; Billings, Stephen A. 16 2015 An iterative orthogonal forward regression algorithm. Zbl 1312.93108Guo, Yuzhu; Guo, L. Z.; Billings, S. A.; Wei, Hua-Liang 7 2015 Approximate observability of infinite dimensional bilinear systems using a Volterra series expansion. Zbl 1305.93037Guo, L. Z.; Guo, Y. Z.; Billings, S. A.; Coca, D. 1 2015 Identification and frequency domain analysis of non-stationary and nonlinear systems using time-varying NARMAX models. Zbl 1332.93356He, Fei; Wei, Hua-Liang; Billings, Stephen A. 1 2015 A parametric frequency response method for non-linear time-varying systems. Zbl 1317.93183Guo, Yuzhu; Guo, L. Z.; Billings, S. A.; Coca, Daniel; Lang, Z. Q. 1 2014 A spatial frequency domain analysis of the Belousov-Zhabotinsky reaction. Zbl 1296.93120Guo, Lingzhong; Guo, Yuzhu; Zhao, Yifan; Billings, Stephen A.; Coca, Daniel; Lang, Zhiqiang 1 2014 Nonlinear system identification. NARMAX methods in the time, frequency, and spatio-temporal domains. Zbl 1287.93101Billings, Stephen A. 71 2013 Volterra series approximation of a class of nonlinear dynamical systems using the Adomian decomposition method. Zbl 1281.37027Guo, Yuzhu; Guo, L. Z.; Billings, S. A.; Coca, Daniel; Lang, Z. Q. 5 2013 The use of Volterra series in the analysis of the nonlinear Schrödinger equation. Zbl 1281.35074Guo, L. Z.; Guo, Y. Z.; Billings, S. A.; Coca, D.; Lang, Z. Q. 3 2013 A Volterra series representation for a class of nonlinear infinite dimensional systems with periodic boundary conditions. Zbl 1259.93068Guo, L. Z.; Guo, Y. Z.; Billings, S. A.; Coca, D.; Lang, Z. Q. 2 2013 A Volterra series approach to the frequency domain analysis of non-linear viscous Burgers’ equation. Zbl 1268.93105Guo, L. Z.; Guo, Y. Z.; Billings, S. A.; Coca, D.; Lang, Z. Q. 3 2012 Nonlinear influence in the frequency domain: alternating series. Zbl 1215.93061Jing, Xing Jian; Lang, Zi Qiang; Billings, Stephen A. 2 2011 Bayesian identification of stochastic linear systems with observations at multiple scales. Zbl 1230.93093Guo, L. Z.; Billings, S. A.; Coca, D.; Balikhin, M. 1 2011 Spatio-temporal modeling of wave formation in an excitable chemical medium based on a revised FitzHugh – Nagumo model. Zbl 1210.35294Zhao, Y.; Billings, S. A.; Guo, Y.; Coca, D.; Dematos, L. L.; Ristic, R. I. 1 2011 Identification of excitable media using a scalar coupled map lattice model. Zbl 1196.93018Guo, Yuzhu; Zhao, Yifan; Billings, S. A.; Coca, Daniel; Ristic, R. I.; Dematos, L. L. 2 2010 Identification of partial differential equation models for a class of multiscale spatio-temporal dynamical systems. Zbl 1184.93034Guo, L. Z.; Billings, S. A.; Coca, D. 1 2010 Suppressing resonant vibrations using nonlinear springs and dampers. Zbl 1273.70067Zhang, Bin; Billings, Stephen A.; Lang, Zi-Qiang; Tomlinson, Geoffrey R. 4 2009 Improved model identification for non-linear systems using a random subsampling and multifold modelling (RSMM) approach. Zbl 1154.93441Wei, H. L.; Billings, S. A. 3 2009 Frequency-dependent magnitude bounds of the generalized frequency response functions for NARX model. Zbl 1298.93235Jing, Xing Jian; Lang, Zi Qiang; Billings, Stephen A. 3 2009 Determination of the analytical parametric relationship for output spectrum of Volterra systems based on its parametric characteristics. Zbl 1152.93044Jing, Xingjian; Lang, Ziqiang; Billings, Stephen A. 2 2009 Improved parameter estimates for non-linear dynamical models using a bootstrap method. Zbl 1175.93220Wei, H. L.; Billings, S. A. 2 2009 Parametric characteristic analysis for generalized frequency response functions of nonlinear systems. Zbl 1175.93153Jing, Xing Jian; Lang, Zi Qiang; Billings, Stephen A. 2 2009 Power-law behaviour evaluation from foreign exchange market data using a wavelet transform method. Zbl 1233.91109Wei, H. L.; Billings, S. A. 1 2009 Identification of multiscale spatio-temporal dynamical systems using a wavelet multiresolution analysis. Zbl 1292.93136Guo, L. Z.; Billings, S. A.; Coca, D. 1 2009 Frequency domain analysis for non-linear Volterra systems with a general non-linear output function. Zbl 1152.93428Jing, X. J.; Lang, Z. Q.; Billings, S. A. 6 2008 An adaptive orthogonal search algorithm for model subset selection and non-linear system identification. Zbl 1152.93343Billings, S. A.; Wei, H. L. 6 2008 Mapping from parametric characteristics to generalized frequency response functions of non-linear systems. Zbl 1152.93429Jing, Xing Jian; Lang, Zi Qiang; Billings, Stephen A. 5 2008 Identification and analysis of spatio-temporal dynamical systems using wavelets. Zbl 1168.93332Guo, L. Z.; Billings, S. A. 4 2008 The identification of complex spatiotemporal patterns using coupled map lattice models. Zbl 1147.37305Pan, Y.; Billings, S. A. 4 2008 Magnitude bounds of generalized frequency response functions for nonlinear Volterra systems described by NARX model. Zbl 1283.93194Jing, Xing Jian; Lang, Zi Qiang; Billings, Stephen A. 4 2008 An extended orthogonal forward regression algorithm for system identification using entropy. Zbl 1152.93507Guo, L. Z.; Billings, S. A.; Zhu, D. Q. 3 2008 Generalized cellular neural networks (GCNNs) constructed using particle swarm optimization for spatio-temporal evolutionary pattern identification. Zbl 1165.68437Wei, H. L.; Billings, S. A. 2 2008 Output frequency response function of nonlinear Volterra systems. Zbl 1117.93047Lang, Z. Q.; Billings, S. A.; Yue, R.; Li, J. 21 2007 Generalized multiscale radial basis function networks. Zbl 1254.68197Billings, Stephen A.; Wei, Hua-Liang; Balikhin, Michael A. 8 2007 New bound characteristics of NARX model in the frequency domain. Zbl 1115.93066Jing, X. J.; Lang, Z. Q.; Billings, S. A. 8 2007 Identification of excitable media using cellular automata models. Zbl 1117.37044Zhao, Y.; Billings, S. A.; Routh, Alexander F. 3 2007 Identification of the Belousov-Zhabotinskii reaction using cellular automata models. Zbl 1136.92017Zhao, Y.; Billings, S. A.; Routh, Alexander F. 2 2007 Analysis of output frequencies of nonlinear systems. Zbl 1390.93556Wu, Xiaofeng; Lang, Z. Q.; Billings, S. A. 1 2007 State-space reconstruction and spatio-temporal prediction of lattice dynamical systems. Zbl 1366.93124Guo, Lingzhong; Billings, Stephen A. 1 2007 A modified orthogonal forward regression least-squares algorithm for system modelling from noisy regressors. Zbl 1120.93018Guo, L.; Billings, S. A. 1 2007 Model validation of spatiotemporal systems using correlation functions test. Zbl 1148.37042Pan, Y.; Billings, S. A. 1 2007 The parametric characteristic of frequency response functions for nonlinear systems. Zbl 1125.93048Jing, Xing Jian; Lang, Zi Qiang; Billings, Stephen A.; Tomlinson, Geofrey R. 12 2006 Identification of coupled map lattice models for spatio-temporal patterns using wavelets. Zbl 1109.92001Billings, S. A.; Guo, L. Z.; Wei, H. L. 4 2006 Wavelet based non-parametric NARX models for nonlinear input-output system identification. Zbl 1129.93361Wei, H. L.; Billings, S. A.; Balikhin, M. A. 4 2006 Estimation of spatial derivatives and identification of continuous spatio-temporal dynamical systems. Zbl 1125.93333Guo, L. Z.; Billings, S. A.; Wei, H. L. 3 2006 Analysis of fast-sampled non-linear systems: generalised frequency response functions for \(\delta \)-operator models. Zbl 1172.94382Chadwick, M. A.; Kadirkamanathan, V.; Billings, S. A. 3 2006 Generalized frequency response functions and output response synthesis for MIMO nonlinear systems. Zbl 1122.93058Li, L. M.; Billings, S. A. 1 2006 A new method for the design of energy transfer filters. Zbl 1330.93232Wu, X.; Lang, Z. Q.; Billings, S. A. 1 2006 Energy transfer properties of non-linear systems in the frequency domain. Zbl 1088.93012Lang, Z. Q.; Billings, S. A. 12 2005 An investigation into the characteristics of nonlinear frequency response functions. I: Understanding the higher dimensional frequency spaces. Zbl 1121.93030Yue, R.; Billings, S. A.; Lang, Z.-Q. 10 2005 The wavelet-NARMAX representation: a hybrid model structure combining polynomial models with multiresolution wavelet decompositions. Zbl 1068.93004Billings, S. A.; Wei, H. L. 9 2005 An investigation into the characteristics of nonlinear frequency response functions. II: New analysis methods based on symbolic expansions and graphical techniques. Zbl 1122.93037Yue, Rong; Billings, S. A.; Lang, Z.-Q. 2 2005 Discrete time subharmonic modelling and analysis. Zbl 1090.93003Li, L. M.; Billings, S. A. 2 2005 A new fast cellular automata orthogonal least-squares identification method. Zbl 1121.93049Billings, S. A.; Mei, S. S. 1 2005 Term and variable selection for nonlinear system identification. Zbl 1050.93506Wei, H. L.; Billings, S. A.; Liu, J. 17 2004 Identification and reconstruction of chaotic systems using multiresolution wavelet decompositions. Zbl 1085.93022Wei, H. L.; Billings, S. A. 9 2004 A unified wavelet-based modelling framework for nonlinear system identification: the WANARX model structure. Zbl 1143.93312Wei, H. L.; Billings, S. A. 5 2004 Identification of coupled map lattice models of stochastic spatio-temporal dynamics using wavelets. Zbl 1072.93028Guo, L. Z.; Billings, S. A. 4 2004 Subharmonic oscillation modeling and MISO Volterra series. Zbl 1368.94174Boaghe, Otilia M.; Billings, Stephen A. 5 2003 Analysis and reconstruction of stochastic coupled map lattice models. Zbl 1028.60035Coca, Daniel; Billings, Stephen A. 3 2003 A new direct approach of computing multi-step ahead predictions for nonlinear models. Zbl 1047.93046Lee, K. L.; Billings, S. A. 2 2003 Identification of finite-dimensional models of infinite-dimensional dynamical systems. Zbl 1011.93026Coca, Daniel; Billings, Stephen A. 11 2002 Nonlinear systems in the frequency domain: Energy transfer filters. Zbl 1038.93064Billings, S. A.; Lang, Zi-Qiang 10 2002 Identification of time-varying systems using multiresolution wavelet models. Zbl 1092.93012Wei, Hua-Liang; Billings, S. A. 7 2002 Time series prediction using support vector machines, the orthogonal and the regularized orthogonal least-squares algorithms. Zbl 1013.93055Lee, K. L.; Billings, S. A. 5 2002 Effects of overparametrization in nonlinear system identification and neural networks. Zbl 1021.93007Zheng, G. L.; Billings, S. A. 1 2002 Identification of coupled map lattice models of complex spatio-temporal patterns. Zbl 0971.37022Coca, D.; Billings, S. A. 16 2001 Generalized frequency response function matrix for MIMO nonlinear systems. Zbl 1038.93066Swain, A. K.; Billings, S. A. 12 2001 Nonlinear system identification using wavelet multiresolution models. Zbl 1024.93061Coca, D.; Billings, S. A. 10 2001 Continuous time nonlinear system identification in the frequency domain. Zbl 1010.93030Li, L. M.; Billings, S. A. 6 2001 Continuous-time system identification using shifted Chebyshev polynomials. Zbl 1059.93503Li, L. M.; Billings, S. A. 1 2001 Direct parameter identification of distributed parameter systems. Zbl 1080.93531Coca, D.; Billings, S. A. 7 2000 Evaluation of output frequency responses of nonlinear systems under multiple inputs. Zbl 0980.93050Lang, Zi-Qiang; Billings, S. A. 6 2000 Multi-directional model validity tests for nonlinear system identification. Zbl 1028.93029Mao, K. Z.; Billings, S. A. 5 2000 Nonlinear system identification using wavelet networks. Zbl 1080.93577Liu, G. P.; Billings, S. A.; Kadirkamanathan, V. 4 2000 Reconstruction of linear and non-linear continuous-time system models from input/output data using the kernel invariance algorithm. Zbl 1237.93175Billings, S. A.; Li, L. M. 2 2000 Discrete wavelet models for identification and qualitative analysis of chaotic systems. Zbl 0955.93502Billings, S. A.; Coca, D. 15 1999 Neural network-based variable structure control for nonlinear discrete systems. Zbl 1015.93504Liu, G. P.; Kadirkamanathan, V.; Billings, S. A. 5 1999 Qualitative validation and generalization in non-linear system identification. Zbl 0941.93511Zheng, G. L.; Billings, S. A. 4 1999 An enhanced sequential fuzzy clustering algorithm. Zbl 1113.62334Zheng, G. L.; Billings, S. A. 2 1999 A regularized rational model estimation algorithm. Zbl 1049.93523Mao, K. Z.; Billings, S. A.; Zhu, Q. M. 1 1999 Predictive control for nonlinear systems using neural networks. Zbl 0948.90053Liu, G. P.; Kadirkamanathan, V.; Billings, S. A. 7 1998 On overparametrization of nonlinear discrete systems. Zbl 0933.37055Mendes, Eduardo M. A. M.; Billings, S. A. 4 1998 Algorithms for minimal model structure detection in nonlinear dynamic system identification. Zbl 0889.93017Mao, K. Z.; Billings, S. A. 16 1997 Output frequencies of nonlinear systems. Zbl 0886.93042Lang, Zi-Qiang; Billings, S. A. 13 1997 Continuous-time system identification for linear and nonlinear systems using wavelet decompositions. Zbl 0925.93153Coca, D.; Billings, S. A. 12 1997 Givens rotation based fast backward elimination algorithm for RBF neural network pruning. Zbl 0885.93025Hong, X.; Billings, S. A. 6 1997 On identifying global nonlinear discrete models from chaotic data. Zbl 0976.93501Mendes, Eduardo M. A. M.; Billings, S. A. 4 1997 Truncation of nonlinear system expansions in the frequency domain. Zbl 0895.93031Billings, S. A.; Lang, Zi-Qiang 4 1997 Output frequency characteristics of nonlinear systems. Zbl 0860.93023Lang, Ziqiang; Billings, S. A. 29 1996 Fast orthogonal identification of nonlinear stochastic models and radial basis function neural networks. Zbl 0858.93069Zhu, Q. M.; Billings, S. A. 12 1996 A bound for the magnitude characteristics of nonlinear ouput frequency response functions. I: Analysis and computation. Zbl 0870.93031Billings, S. A.; Lang, Zi-Qiang 6 1996 Gain bounds of higher-order nonlinear transfer functions. Zbl 0860.93013Zhang, H.; Billings, S. A. 5 1996 Decomposition of generalized frequency response functions for nonlinear systems using symbolic computation. Zbl 0870.93033Billings, S. A.; Yusof, M. I. 4 1996 Smoothing data with local instabilities for the identification of chaotic systems. Zbl 0847.93025Aguirre, Luis A.; Mendes, Eduardo M.; Billings, S. A. 2 1996 A bound for the magnitude characteristics of nonlinear output frequency response functions. II: Practical computation of the bound for systems described by the nonlinear autoregressive model with exogenous input. Zbl 0870.93032Billings, S. A.; Lang, Zi-Qiang 2 1996 Stable sequential identification of continuous nonlinear dynamical systems by growing radial basis function networks. Zbl 0856.93026Liu, G. P.; Kadirkamanathan, V.; Billings, S. A. 2 1996 ...and 73 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,382 Authors 135 Billings, Stephen A. 24 Aguirre, Luis Antonio 24 Zhu, Quanmin 23 Guo, Lingzhong 22 Coca, Daniel 20 Wei, Hualiang 18 Chen, Sheng 16 Lang, Ziqiang 16 Schoukens, Johan 15 Letellier, Christophe 14 Jing, Xingjian 12 Guo, Yuzhu 10 Li, Kang 9 Jones, J. C. Peyton 9 Peng, Zhike 8 Kadirkamanathan, Visakan 8 Nepomuceno, Erivelton Geraldo 8 Piroddi, Luigi 8 Zinober, Alan Solon Ivor 7 Bai, Erwei 7 Brunton, Steven L. 7 Irwin, George William 7 Krzyżak, Adam 7 Ljung, Lennart 7 Mangiarotti, Sylvain 7 Meng, Guang 7 Pintelon, Rik 7 Tsang, Kai Ming 7 Zhao, Yifan 6 Ding, Feng 6 Maquet, Jean 6 Mendes, Eduardo M. A. M. 6 Zhang, Wenming 5 Anderson, Sean R. 5 Chen, Jing 5 Greblicki, Wlodzimierz 5 Hasiewicz, Zygmunt 5 Hong, Xia 5 Kutz, J. Nathan 5 Leontaritis, I. J. 5 Mzyk, Grzegorz 5 Schoukens, Maarten 5 Suykens, Johan A. K. 5 Tiels, Koen 5 Wang, Liuping 5 Żak, Stanislaw H. 4 Chen, Guanrong 4 Cheng, Changming 4 Hjalmarsson, Håkan 4 Hui, Stefen 4 Kenné, Godpromesse 4 Lamnabhi-Lagarrigue, Françoise 4 Liu, Yanjun 4 Martins, Samir A. M. 4 Mitchell, R. J. 4 Rolain, Yves 4 Shyu, Kuo-Kai 4 Takahashi, Ricardo H. C. 4 Unbehauen, Heinz 4 Wang, Cong 4 Zhu, Yunpeng 3 Agamennoni, Osvaldo E. 3 Bianchi, Federico 3 Chen, C. L. Philip 3 Dewson, T. 3 Elad, Michael 3 Ge, Shuzhi Sam 3 Huc, Mireille 3 Irving, Andrew D. 3 Jafari, Sajad 3 Janczak, Andrzej 3 Kukreja, Sunil L. 3 Lee, Tong Heng 3 Li, Xiuting 3 Longden, Ashley 3 Marmarelis, Vasilis Z. 3 Mei, Shuaishuai 3 Nešić, Dragan 3 Panahi, Shirin 3 Partyka, Marian A. 3 Pawlak, Mirosław 3 Piga, Dario 3 Prandini, Maria 3 Rodin, Ervin Y. 3 Şendrescu, Dorin 3 Śliwiński, Przemysław 3 Steinbuch, Maarten 3 Tang, Xiaoquan 3 Teel, Andrew Richard 3 Tsai, Yao-Wen 3 Vanbeylen, Laurent 3 Vandersteen, Gerd 3 Voon, W. S. F. 3 Xu, Daolin 3 Yue, Rong 3 Zhang, Lifeng 3 Zhang, Long 3 Zhang, Weicun 3 Zhao, Dongya 2 Abdalmoaty, Mohamed Rasheed-Hilmy ...and 1,282 more Authors all top 5 Cited in 129 Serials 125 International Journal of Control 116 Automatica 89 International Journal of Systems Science 37 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 37 International Journal of Systems Science. 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Mathematical, Physical and Engineering Sciences 4 Circuits, Systems, and Signal Processing 4 Journal of Nonlinear Science 4 Applied and Computational Harmonic Analysis 4 Journal of Control Science and Engineering 3 Computer Methods in Applied Mechanics and Engineering 3 Journal of Computational Physics 3 Journal of Fluid Mechanics 3 Journal of Computational and Applied Mathematics 3 Kybernetika 3 Meccanica 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 MCSS. Mathematics of Control, Signals, and Systems 3 Journal of Statistical Computation and Simulation 3 Soft Computing 3 Acta Mechanica Sinica 2 Biological Cybernetics 2 Computers & Mathematics with Applications 2 Physics Letters. A 2 Dynamics and Control 2 Computational Statistics 2 Communications in Statistics. Simulation and Computation 2 Linear Algebra and its Applications 2 Pattern Recognition 2 Journal of Computational Neuroscience 2 Abstract and Applied Analysis 2 Journal of Applied Mathematics 2 Journal of Machine Learning Research (JMLR) 2 SIAM Journal on Applied Dynamical Systems 2 Journal of Control Theory and Applications 2 Inverse Problems in Science and Engineering 2 Nonlinear Analysis. Theory, Methods & Applications 1 Computers and Fluids 1 International Journal for Numerical Methods in Fluids 1 Inverse Problems 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Biology 1 Physica A 1 Bulletin of Mathematical Biology 1 Theoretical and Computational Fluid Dynamics 1 Canadian Mathematical Bulletin 1 Journal of Approximation Theory 1 Journal of Econometrics 1 Numerical Functional Analysis and Optimization 1 SIAM Journal on Control and Optimization 1 Theoretical Population Biology 1 Optimal Control Applications & Methods 1 Cybernetics and Systems 1 International Journal of Production Research 1 Constructive Approximation 1 International Journal of Approximate Reasoning 1 Journal of Scientific Computing 1 Signal Processing 1 Machine Learning 1 Communications in Statistics. Theory and Methods 1 European Journal of Operational Research 1 International Journal of Computer Mathematics 1 Computational Statistics and Data Analysis 1 Archive of Applied Mechanics 1 Advances in Engineering Software 1 Computational Optimization and Applications 1 Physics of Fluids 1 Computational and Applied Mathematics 1 Fractals 1 ETNA. Electronic Transactions on Numerical Analysis 1 Matematychni Metody ta Fizyko-Mekhanichni Polya 1 Neural Computing and Applications 1 Multibody System Dynamics 1 Journal of Applied Statistics 1 Higher-Order and Symbolic Computation ...and 29 more Serials all top 5 Cited in 32 Fields 619 Systems theory; control (93-XX) 95 Statistics (62-XX) 93 Biology and other natural sciences (92-XX) 90 Dynamical systems and ergodic theory (37-XX) 85 Computer science (68-XX) 73 Numerical analysis (65-XX) 35 Ordinary differential equations (34-XX) 29 Operations research, mathematical programming (90-XX) 29 Information and communication theory, circuits (94-XX) 25 Mechanics of particles and systems (70-XX) 22 Partial differential equations (35-XX) 13 Calculus of variations and optimal control; optimization (49-XX) 12 Fluid mechanics (76-XX) 11 Probability theory and stochastic processes (60-XX) 11 Mechanics of deformable solids (74-XX) 9 Approximations and expansions (41-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 6 Statistical mechanics, structure of matter (82-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Operator theory (47-XX) 5 Geophysics (86-XX) 4 Real functions (26-XX) 3 Integral equations (45-XX) 2 General and overarching topics; collections (00-XX) 2 Difference and functional equations (39-XX) 1 History and biography (01-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Manifolds and cell complexes (57-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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