Adaptive identifier for uncertain complex-valued discrete-time nonlinear systems based on recurrent neural networks

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• 作者：M. Alfaro-Ponce ; I. Salgado ; A. Arguelles ; I. Chairez
• 关键词：Complex ; valued systems ; Non ; parametric modeling ; Recurrent neural networks ; Lyapunov control functions
• 刊名：Neural Processing Letters
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：43
• 期：1
• 页码：133-153
• 全文大小：2,948 KB
• 参考文献：1.Aibinu A, Salami J, Shafie A (2010) Determination of complex valued parametric model coefficients using artificial neural network technique. Adv Artif Neural Syst 2010:11
  2.Aizenberg I (2011) Complex valued neural networks with multi-valued neurons. Springer, BerlinCrossRef MATH
  3.Aizenberg N, Ivaskiv L, Pospelov A (1971) About one generalization of the threshols function. Dokl Akad Nauk 196(6):1287–1290MathSciNet
  4.Axler S, Ribet KA (2010) Complex analysis. Springer, New York
  5.Benvenuto N, Dinis R, Falconer D, Tomasin S (2010) Single carrier modulation with nonlinear frequency domain equalization: an idea whose time has come-again. Proc IEEE 98(1):69–96CrossRef
  6.Benvenuto N, Piazza F (1992) On the complex backpropagation algorithm. IEEE Trans Signal Process 40(4):967–969CrossRef
  7.Chairez I (2009) Wavelet differential neural network. IEEE Trans Neural Netw 20:1439–1449CrossRef
  8.Cotter NE (1990) The stone-weierstrass theorem and its application to neural networks. IEEE Trans Nueral Netw 1(4):290–295MathSciNet CrossRef
  9.Dong-Chul P, Tae-Kyun J (2002) Complex bilinear recurrent neural network for equalization of a digital satellite channel. IEEE Trans Nueral Netw 13(3):711–725CrossRef
  10.Egmont-Petersen M, Ridder D, Handels H (2002) Image processing with neural networks: a review. Pattern Recognit 35(10):2279–2301CrossRef MATH
  11.Freeman RA, Kokotovic PV (2008) Robust nonlinear control design. Birkhauser, BostonMATH
  12.Georgiou G, Koutsougeras C (1992) Complex domain backpropagation. IEEE Trans Circuits Syst 39(5):330–334CrossRef MATH
  13.Gompper G, Ihle T, Kroll D, Winkler RG (2008) Advances in polymer science, chap. multi particle collision dynamics: a particle-based mesoscale simulation approach to the hydrodynamics of complex fluids. Springer, Berlin
  14.Han S, Lee K (2010) Robust friction state observer and recurrent fuzzy neural network design for dynamic friction compensation with backstepping control. Mechatronics 20(3):384–401CrossRef
  15.Hernandez-Vargas E, Alanis A, Sanchez E (2012) Discrete-time neural observer for hiv infection dynamics. In: World Automation Congress (WAC)
  16.Hirose A (2012) Complex valued neural networks. Springer, BerlinCrossRef MATH
  17.Hussain Z, Sadik A, Shea P (2011) Digital signal processing and introduction with mathlab and applications, chap. 2 Discrte and digital signals and systems. Springer, Berlin
  18.J D, Sundararajan N, Saratchandran P (2002) Communication channel equalization using complex valued minimal radial basis function neural networks. IEEE Trans Neural Netw 13(3):687–696CrossRef
  19.Kim T, Adali T (2003) Approximation by fully complex multilayer perceptrons. Neural Comput 15(7):16411666CrossRef
  20.Kobayashi M, Yamazaki H (2003) Information geometry of complex-valued boltzmann machines. IEICE Trans Fundam Electron Commun Comput Sci J87–A(8):1093–1101
  21.Kuroe Y (2003) Complex-valued neural networks: theories and applications, chap. a model of complex-valued associative memories and its dynamics. World Scientific Pub Co Inc., River Edge
  22.Lakshmikantham V, Matrosov VM, Sivasundaram (1991) Vector Lyapunov functions and stability analysis of nonlinear systems. Kluwer, AmsterdamCrossRef MATH
  23.Lee S, Mandic D (2006) An augmented extended kalman filter algorithm for complex-valued recurrent neural networks. In: IEEE International Conference on Acoustics, speech and signal processing (ICASSP)
  24.Lee Goh S, Mandic DP (2004) A complex-valued rtrl algorithm for recurrent neural networks. Neural Comput 16(12):2699–2713CrossRef MATH
  25.Lee Goh S, Mandic DP (2007) An augmented crtrl for complex-valued recurrent neural networks. Neural Netw 20:1061–1066CrossRef MATH
  26.Leung H, Haykin S (1991) Complex domain backpropagation. IEEE Trans Signal Process 39(9):2101–2104CrossRef
  27.Mandic D, Su Lee Goh V (2009) Complex valued nonlinear adaptive filters. Wiley, ChichesterCrossRef
  28.McLachlan MW (2010) Complex variable theory and transform calculus: with technical applications. Cambridge University Press, Cambridge
  29.Nitta T (1997) An extension of the back-propagation algorithm to complex-numbers. Neural Netw 10(8):1391–1415CrossRef
  30.Nitta T (2000) And analysis of the fundamental structure of complex valued neurons. Neural Process Lett 12:239–246CrossRef MATH
  31.Noest AJ (1988) Discrete-state phasor neural networks. Phys Rev A 38:2196–2199CrossRef
  32.Noest AJ (1988) Phasor neural networks. Neural information processing systems. AIP, New York, pp 584–591
  33.Oppenheim A, Lim J (1981) The importance of phase in signals. Proc IEEE 69(5):529–541CrossRef
  34.Peng M, Chen S, Guanglin Y (2012) Proceedings of the international conference on information engineering and applications, chap. 74 Sparser signals and compressive sampling based on FFT and DWT Peng. Springer, London, pp 619–624
  35.Poznyak A, Sanchez E, Yu W (2001) Differential neural networks for robust nonlinear control (identification, state estimation an trajectory tracking. World Scientific, River EdgeCrossRef
  36.Poznyak AS, Medel J (1999) Matrix forgetting factor. Int J Syst Sci 30(2):165–174CrossRef MATH
  37.Rizek S, Kucera M (1999) Hard-limits neural nets with electrooptical elements. Neural Netw World 9(6):417–487
  38.Salgado I, Chairez I (2009) Discrete time recurrent neural network observer. In: 2009 International Joint Conference on Neural Networks, pp 909–916
  39.Salgado I, Chairez I (2013) Discrete-time recurrent neural network observer. Neurocomputing 101:73–81CrossRef
  40.Tanaka T, Mandic D (2007) Complex empirical mode decomposition. IEEE Signal Process Lett 14(2):101–104CrossRef
  41.Wang Z, Liu Y, Liu X (2009) State estimation for jumping recurrent neural networks with discrete and distributed delays. Neural Netw 22(1):41–48CrossRef
  42.Wen S, Zeng Z, Haung T, Chen Y (2013) Passivity analysis of memristor-based recurrent neural networks with time-varying delays. J Frankl Inst 350(8):2354–2370CrossRef MATH
  43.Xia Y, Jelfs B, Van Hulle MM, Principe J, Mandic DP (2011) An augmented echo state network for nonlinear adaptive filtering of complex noncircular signals. IEEE Trans Neural Netw 22:74–83CrossRef
  44.Zhou J, Gao S (2013) An esperimental study on the auto-association neural network with electronic image processing. LNEE 178(3)(1):395–401
  
• 作者单位：M. Alfaro-Ponce (1)
  I. Salgado (1)
  A. Arguelles (1)
  I. Chairez (2)
  
  1. Neural networks and non-conventional computing laboratory, Instituto Politecnico Nacional, Centro de Investigacion en Computacion, Ciudad de Mexico, Mexico
  2. Bioprocess Department, Unidad Profesional Interdisciplinaria de Biotecnologia, Instituto Politecnico Nacional, Ciudad de Mexico, Mexico
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Complexity
  Artificial Intelligence and Robotics
  Electronic and Computer Engineering
  Operation Research and Decision Theory
  
• 出版者：Springer Netherlands
• ISSN：1573-773X

文摘

Recently, the study of dynamic systems and signals in the frequency domain motivates the emergence of new tools. In particular, electrophysiological and communications signals in the complex domain can be analyzed but hardly, they can be modeled. This problem promotes an attractive field of researching in system theory. As a consequence, adaptive algorithms like neural networks are interesting tools to deal with the identification problem of this kind of systems. In this study, a new learning process for recurrent neural network applied on complex-valued discrete-time nonlinear systems is proposed. The Lyapunov stability framework is applied to obtain the corresponding learning laws by means of the so-called Lyapunov control functions. The region where the identification error converges is defined by the power of uncertainties and perturbations that affects the nonlinear discrete-time complex system. This zone is obtained as an alternative result of the same Lyapunov analysis. An off-line training algorithm is derived in order to reduce the size of the convergence zone. The training is executed using a set of some off-line measurements coming from the uncertain system. Numerical results are developed to prove the efficiency of the methodology proposed in this study. A first example is oriented to identify the dynamics of a nonlinear discrete time complex-valued system and the second one to model the dynamics of an electrophysiological signal separated in magnitude and phase. Keywords Complex-valued systems Non-parametric modeling Recurrent neural networks Lyapunov control functions