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Cooperative recurrent modular neural networks for constrained optimization: a survey of models and applications

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Abstract

Constrained optimization problems arise in a wide variety of scientific and engineering applications. Since several single recurrent neural networks when applied to solve constrained optimization problems for real-time engineering applications have shown some limitations, cooperative recurrent neural network approaches have been developed to overcome drawbacks of these single recurrent neural networks. This paper surveys in details work on cooperative recurrent neural networks for solving constrained optimization problems and their engineering applications, and points out their standing models from viewpoint of both convergence to the optimal solution and model complexity. We provide examples and comparisons to shown advantages of these models in the given applications.

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References

  • Agganwal JK (1993) Multisensor fusion for computer vision. Springer-Verlag, Berlin

  • Alexandre LA, Campilho AC, Kamel M (2001) On combining classifiers using sum and product rules. Pattern Recognit Lett 22:1283–1289

    Article  Google Scholar 

  • Alliney S, Ruzinsky SA (1994) An algorithm for the minimization of mixed L 1 and L 2 norms with application to bayesian-estimation. IEEE Trans Signal Process 42:618–627

    Article  Google Scholar 

  • Al-Smadi A, Alshamali A (2002) Fitting ARMA models to linear non-Gaussian processes using higher order statistics. Signal Processing 82:1789–1793

    Article  Google Scholar 

  • Anand R, Mehrotra K, Mohan CK, Ranka S (1995) Efficient classification for multiclass problems using modular neural networks. IEEE Trans Neural Netw 6:117–124

    Article  PubMed  CAS  Google Scholar 

  • Andrews HC, Hunt BR (1977) Digital image restoration. Prentice-Hall, New York

    Google Scholar 

  • Anguita D, Boni A (2002) Improved neural network for SVM learning. IEEE Trans Neural Netw 13:1243–1244

    Article  PubMed  CAS  Google Scholar 

  • Anzai Y, Shimada T (1988) Modular neural networks for shape and/or location recognition. Int Neural Network Soc First Ann Meeting, Boston, USA, 158 pp

  • Arteage-Bravo FJ (1990) Multilayer backpropagation network for learning the forward and inverse kinematics equations. Proc Int Conf Neural Netw, vol II, Washington, DC, pp 319–322

  • Auda G, Kamel MS (1997a) CMNN: cooperative modular neural network. Int Conf Neural Netw 1:226–231

    Google Scholar 

  • Auda G, Kamel MS (1997b) CMNN: cooperative modular neural networks for pattern recognition. Pattern Recognit Lett 18:1391–1398

    Article  Google Scholar 

  • Auda G, Kamel MS (1998a) Modular neural network classifiers: a comparative study. J Intell Robotic Syst 21:117–129

    Article  Google Scholar 

  • Auda G, Kamel MS (1998b) CMNN: cooperative modular neural network. Neurocomputing 20:189–207

    Article  Google Scholar 

  • Auda G, Kamel MS (1999) Modular neural networks: a survey. Int J Neural Syst 9:129–151

    Article  PubMed  CAS  Google Scholar 

  • Avitzour D (1992) A maximum likehood approach to data association. IEEE Trans AES 28(2):560–566

    Google Scholar 

  • Baker DR, Wampler CW II (1988) On the inverse kinematics of redundant manipulators. Int J Robot Res 7:3–21

    Article  Google Scholar 

  • Bazaraa MS, Sherali HD, Shetty CM (1993) Nonlinear programming – theory and algorithms, 2nd edn. Wiley, New York

    Google Scholar 

  • Bekey GA (1992) Robotics and neural networks. In: Kosko B (ed) Neural networks for signal processing. Prentice-Hall, Englewood, pp 161–185

    Google Scholar 

  • Broomhead DS, Lowe D (1988) Multivariable functional interpolation and adaptive networks. Complex Syst 2:321–355

    Google Scholar 

  • Burges CJ (1998) A tutorial on support vector machines for patter recognition. Data Mining Knowl Discov 2(2):1–47

    Article  Google Scholar 

  • Caelli T, Guan L, Wen W (1999) Modularity in neural computing. Proc IEEE 87:1497–1518

    Article  Google Scholar 

  • Chang PR, Yang WH, Chan KK (1992) A neural network approach to MVDR beamforming problem. IEEE Trans Antennas Propagation 40:313–322

    Article  Google Scholar 

  • Chen S, Billings SA (1992) Neural networks for nonlinear dynamic system modelling and identification. Int J Control 56:319–346

    Article  Google Scholar 

  • Chen LJ, Narendra KS (2004) Identification and control of a nonlinear discrete-time system based on its linearization: a unified framework. IEEE Trans Neural Netw 15:663–673

    Article  PubMed  Google Scholar 

  • Cheng F-T, Chen T-H, Sun Y-Y (1994) Resolving manipulator redundancy under inequality constraints. IEEE J Robot Automat 10(1):65–71

    Article  CAS  Google Scholar 

  • Cheng F-T, Sheu R-J, Chen T-H (1995) The improved compact QP method for resolving manipulator redundancy. IEEE Trans Syst Man Cybern 25(11):1521–1530

    Article  Google Scholar 

  • Cichocki A, Unbehauen R (1993) Neural networks for optimization and signal processing. Wiley, England

    Google Scholar 

  • Copeland M (1995) Modular network control for robot manipulator. Proc IEEE Visualize Future 26–29:183–187

    Google Scholar 

  • Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20:273–297

    Google Scholar 

  • Ding H, Tso SK (1999) A fully neural-network-based planning scheme for torque minimization of redundant manipulators. IEEE Trans Industr Electr 46:199–206

    Article  Google Scholar 

  • Drosopoulos A (1994) Description of the OHGR database. Defence Research Establishment, Ottawa, Ont, Tech. Note 94–14

  • Du KL, Lai AKY, Cheng KKM, Swamy MNS (2002) Neural methods for antenna array signal processing: a review. Signal Processing 82:547–561

    Article  Google Scholar 

  • Durrant-Whyte HF (1985) Integrating distributed sensor information: an application to robot system coordinate. Proc IEEE Int Conf Syst Man Cyber, pp 415– 419

  • Fiori S (2003) Neural minor component analysis approach to robust constrained beamforming. IEEE Proc Vision Image Signal Process 150:205–218

    Google Scholar 

  • Fogelman-Soulie F (1993) Multi-modular neural network-hybrid architectures: a review. Proc Int Joint Conf Neural Netw 3:25–29

    Google Scholar 

  • Frost OL (1972) An algorithm for linear constrained adaptive array processing. Proc IEEE 60:926–935

    Article  Google Scholar 

  • Fukushima M, Luo ZQ, Tseng P (2003) A sequential quadratically constrained quadratic programming method for differentiable convex minimization. SIAM J Optim 13:1098–1119

    Article  Google Scholar 

  • Galatsanos NP, Katsaggelos AK (1992) Methods for choosing the regularization parameter and estimate the noise variance in image restoration and their relation. IEEE Trans Image Process 1:322–336

    Article  PubMed  CAS  Google Scholar 

  • Gao XB, Liao LZ, Qi LQ (2005) A novel neural network for variational inequalities with linear and nonlinear constraints. IEEE Trans Neural Netw 16:1305–1317

    Article  PubMed  Google Scholar 

  • Giannakis GB, Mendel JM (1990) Cumulant-based order determination of non-Gaussian ARMA models. IEEE Trans Acoust 38:1411–1423

    Article  Google Scholar 

  • Glazos MP, Hui S, Zak SH (1998) Sliding modes in solving convex programming problems. SIAM J Control Optim 36:680–697

    Article  Google Scholar 

  • Guan L, Anderson JA, Sutton JP (1997) A network of networks processing model for image regularization. IEEE Transactions On Neural Networks 8:169–174

    Article  PubMed  CAS  Google Scholar 

  • Guez A, Ahmad Z (1989) Accelerated convergence in the inverse kinematics via multilayer feedforward networks. Proc Int Conf Neural Netw, vol II, Washington, DC, pp 341–344

  • Hansen LK, Salamon P (1990) Neural network ensembles. IEEE Trans Pattern Anal Mach Intell 12:993–1002

    Article  Google Scholar 

  • Hashem S (1997) Optimal linear combination of neural networks. Neural Netw 10:599–614

    Article  PubMed  Google Scholar 

  • Haykin S (1994) Neural networks: a comprehensive foundation. Macmillan Publishing, New York

    Google Scholar 

  • He Y, Sun Y (2001) Neural network-based L 1 norm optimization approach for fault diagnosis of nonlinear circuits with tolerance. IEEE Proc Circuit Devices 148:223–229

    Google Scholar 

  • Hodge L, Auda G, Kamel MS (1999) Learning decision fusion in cooperative modular neural networks. Int Joint Conf Neural Netw 4:2777–2781

    Google Scholar 

  • Hong MC, Stathaki T, Katstaggelos AK (2002) Iterative regularized least-mean mixed-norm image restoration. Opt Eng 41:2515–2524

    Article  Google Scholar 

  • Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational ability. Proc Natl Acad Sci USA Biophy 79:2554–2558

    Google Scholar 

  • Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2:359–366

    Article  Google Scholar 

  • Islam MM, Yao X, Murase K (2003) A constructive algorithm for training cooperative neural network ensembles. IEEE Trans Neural Netw 14:820–834

    Article  PubMed  Google Scholar 

  • Jacobs RA, Jordan MI, Barto AG (1991) Task decomposition through competition in modular connectionist architecture: the what and where vision tasks. Conit Sci 15:219–250

    Article  Google Scholar 

  • Kadirkamanathan V, Fabri SG (1998) Recursive structure estimation for nonlinear identification with modular network. Proc IEEE, pp 343–348

  • Kadirkamanathan V, Niranjan M (1993) A function estimation approach to sequential learning with neural networks. Neural Comput 5:954–975

    Article  Google Scholar 

  • Kamel MS (1999) Neural networks: the state of the art. Proceeding of the eleventh international conference on microelectronics, pp 22–24, Nov

  • Katsaggelos AK, Biemond J, Schafer RW, Mersereau RM (1991) A regularized iterative image-restoration algorithm. IEEE Trans Signal Process 39:914–929

    Article  Google Scholar 

  • Kay SM (1993) Fundamentals of statistical signal processing: estimation theory. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Kecman V (1996) System identification using modular neural network with improved learning. Proceedings of International Workshop on Neural Networks for Identification, Control, Robotics, and Signal/Image Processing 21–23:40–48

  • Kehagias A, Petridis V (1997) Predictive modular neural networks for time series classification. Neural Netw 10:31–49

    Article  PubMed  Google Scholar 

  • Kennedy MP, Chua LO (1988) Neural networks for nonlinear programming. IEEE Trans Circuits Syst 35(5):554–562

    Article  Google Scholar 

  • Kinderlehrer D, Stampcchia G (1980) An introduction to variational inequalities and their applications. Academic Press, New York

    Google Scholar 

  • Klein CA, Huang CH (1983) Review of pseudoinverse control for use with kinematically redundant manipulators. IEEE Trans Syst Man Cybern 13:245–250

    Google Scholar 

  • Kohonen T (1989) Self-organization and associative memory, 3rd edn. Springer-verlag, Berlin

    Google Scholar 

  • Koukoulas P, Kalouptsidis N (2000) Second-order Volterra system identification. IEEE Trans Signal Process 48:3574–3577

    Article  Google Scholar 

  • Kuo SS, Mammone JJ (1992) Image-restoration by convex projections using adaptive constraints and L 1 norm estimation. IEEE Trans Signal Process 40:159–168

    Article  Google Scholar 

  • Leung H, Hennessey G, Drosopoulos A (2000) Signal detection using the radial basis function coupled map lattice. IEEE Trans Neural Netw 11(5):1133–1151

    Article  PubMed  CAS  Google Scholar 

  • Leung Y, Chen KZ, Jiao YC et al (2001) A new gradient-based neural network for solving linear and quadratic programming problems. IEEE Trans Neural Netw 12:1074–1083

    Article  PubMed  CAS  Google Scholar 

  • Li W, Swetits JJ (1998) The linear L 1 estimator and the Huber m-estimator. SIAM J Optim 8:457–475

    Article  Google Scholar 

  • Li W, Huang Xinping, Leung H (2004) Performance evaluation of digital beamforming strategies for satellite communications. IEEE Trans Aerosp Electron Syst 40:12–26

    Article  Google Scholar 

  • Ljung L (1999) System identification – theory for the user, 2nd edn. Prentice-Hall, Upper Saddle River

    Google Scholar 

  • Lu BL, Ito M (1999) Task decomposition and module combination based on class relations: a modular neural network for pattern classification. IEEE Trans Neural Netw 10:1244–1250

    Article  PubMed  CAS  Google Scholar 

  • Maa CY, Shanblatt MA (1992) Linear and quadratic programming neural network analysis. IEEE Trans Neural Netw 3:580–594

    Article  PubMed  CAS  Google Scholar 

  • Maciejemski AA, Klein CA (1985) Obstacle avoidance for kinematically redundant manipulators in dynamically varying environments. Int J Robot Res 4(3):109–117

    Article  Google Scholar 

  • Mammone RJ, Rothacker RJ (1987) General iterative method of restoring linearly degraded images. J Opt Soc Am A Opt Image Sci Vis 4:208–215

    Article  Google Scholar 

  • Mangasarian OL, Musicant DR (1999) Successive overrelaxation for support vector machines. IEEE Trans Neural Netw 10:1032–1037

    Article  PubMed  CAS  Google Scholar 

  • McCulloch W, Pitts W (1943) A logical calculus of the ideas imminent in nervous activity. Bull Math Biophys 5:115–133

    Article  Google Scholar 

  • Melin P, Felix C, Castillo O (2005) Face recognition using modular neural networks and the fuzzy Sugeno integral for response integration. Int J Intell Syst 20:275–291

    Article  Google Scholar 

  • Muller KR, Smola AJ, Ratsch G, Schokopf BS, Kohlmorgen J, Vapnik V (1997) Predicting time series with support vector machines. Proceedings of ICANN, Springer, LNCS 1327:999–1004

  • Nehorai A, Stoica P (1988) Adaptive algorithms for constrained ARMA signals in the presence of noise. IEEE Trans Acoust 36:1282–1291

    Article  Google Scholar 

  • Nesterov Y, Nemirovsky A (1994) Interior-point polynomial methods in convex programming. Studies in Applid Mathematics, SIMA, 13

  • Oh IS, Suen CY (2002) A class-modular feedforward neural network for handwriting recognition. Pattern Recognit 35:229–244

    Article  Google Scholar 

  • Oja E (1992) Principal components, minor components and linear neural networks. Neural Netw 5:927–935

    Article  Google Scholar 

  • Ozawa S (1998) An associative memory model derived from cross-coupled Hopfield nets and its role in noise-space dynamics. Electr Eng 117:1253–1258

    Google Scholar 

  • Paik JK, Katsaggelos AK (1992) Image restoration using a modified Hopfield network. IEEE Trans Image Process 1:49–63

    Article  PubMed  CAS  Google Scholar 

  • Perry SW, Guan L (1996) A partitioned modified Hopfield neural network algorithm for real-time image restoration. Real-Time Imaging 2:215–224

    Article  Google Scholar 

  • Reed IS, Mallett JD, Brennan LE (1974) Rapid convergence rate in adaptive arrays. IEEE Trans Aerosp Electron Syst AES-10:853–863

    Article  Google Scholar 

  • Rodríguez-Vázquez A, Domínguez-Castro R, Rueda A, Huertas JL, Sánchez-Sinencio E (1990) Nonlinear switched-capacitor ‘neural networks’ for optimization problems. IEEE Trans Circuits Syst 37:384–397

    Article  Google Scholar 

  • Rojo-Alvarez JL, Martinez-Ramon M, de Prado-Cumplido M, Artes-Rodriguez A, Figueiras-Vidal AR (2004) Support vector method for robust ARMA system identification. IEEE Trans Signal Process 52:155-164

    Article  Google Scholar 

  • Roll J, Nazin AA, Ljung L (2005) Nonlinear system identification via direct weight optimization. Automatica 41:475–490

    Article  Google Scholar 

  • Rumelhart DE, Hinton GE, Williams RJ (1986) Learning internal representations by backpropagating errors. Nature 323:553–536

    Article  Google Scholar 

  • Ruzinsky SA, Olsen ET (1989) L 1 and L minimization via a variant of Karmarkar’s algorithm. IEEE Trans Signal Process 37:245–253

    Google Scholar 

  • Schapire RE (1990) The strength of weak learnability. Mach Learn 5:197–227

    Google Scholar 

  • Sciavicco L, Siciliano B (2000) Modelling and control of robot manipulators. Springer-Verlag London, Great Britain

    Google Scholar 

  • Seraji H, Long MK, Lee TS (1993) Motion control of 7-DOF arms:the configuration control approach. IEEE Trans Rob Autom 4:125–139

    Article  Google Scholar 

  • Sharkey AJC (1998) Combing artfical neural nets: ensemble and modular multi-nets systems. Springer-Verlag, New York

    Google Scholar 

  • Sierra A, Cruz CS (1998) Global and local neural network ensembles. Pattern Recogn Lett 19:651–655

    Article  Google Scholar 

  • Smith KA (1999) Neural networks for combinatorial optimization: a review of more than a decade of research. Informs J Comput 11:15–28

    Article  Google Scholar 

  • Smith RC, Cheesman P (1986) On the representation of estimation and spatial uncertainty. Int J Robot Res 5(1):56–68

    Article  CAS  Google Scholar 

  • Soderstrom T, Stoica P (1981) Comparison of some instrumental variable methods-consistency and accuracy aspects. Automatica 17:101–115

    Article  Google Scholar 

  • Solodov MV, Tseng P (1996) Modified projection-type methods for monotone variational inequalities. SIAM J Control Optim 2:1814–1830

    Article  Google Scholar 

  • Sun Y (2000) Hopfield neural network based algorithms for image restoration and reconstruction – Part I: algorithms and simulations. IEEE Trans Signal Process 48:2105–2118

    Article  Google Scholar 

  • Suykens JAK, Gestel TV, Brabanter JD, Moor BD, Vandewalle J (2002) Least squares support vector machines. World Scientific, Singapore

    Google Scholar 

  • Tan Y, Xia Y, Wang J (2000) Neural network realization of support vector methods for pattern classification. Proc IEEE Int Joint Conf Neural Netw, pp 411–416

  • Tank DW, Hopfield JJ (1986) Simple neural optimization networks: an A/D converter, signal decision circuit, and a linear programming circuit. IEEE Trans Circuits Syst 33(5):533–541

    Article  Google Scholar 

  • Tao Q, Fang TJ (2000) The neural network model for solving minimax problems with constraints. Control Theory Control Appl 17(1):82–84 (Chinese Edition)

    Google Scholar 

  • Tao Q, Cao JD, Xue MS, Qiao H (2001) A high performance neural network for solving nonlinear programming problems with hybrid constraints. Phys Lett A 288(2):88–94

    Article  CAS  Google Scholar 

  • Tekalp AM, Kaufman H, Woods JW (1985) Fast recursive estimation of the parameters of a space-varying autoregressive image model. IEEE Trans Acoust 33:469–472

    Article  Google Scholar 

  • Thompson AM, Brown JC, Kay JW, Titterington DM (1991) A study of methods of choosing the smoothing parameter in image restoration by regularization. IEEE Trans Pattern Anal Mach Intell 13:326–339

    Article  Google Scholar 

  • Tian Z, Bell KL, Van Trees HL (2001) A recursive least squares implementation for LCMP beamforming under quadratic constraint. IEEE Trans Signal Process 49:1138–1145

    Article  Google Scholar 

  • Van Trees HL (1998) Optimum array processing: detection and estimation theory. Class Notes: INFT 836

  • Varshney PK (1997) Multisensor data fusion. J Electron Commun Eng 9:245–253

    Article  Google Scholar 

  • Wang J, Hu Q, Jiang D (1999) A Lagrangian neural network for kinematic control of redundant robot manipulators. IEEE Transactions on Neural Networks 10:1123–1132

    Article  PubMed  CAS  Google Scholar 

  • Wang ZS, Cheung JY, Xia YS, Chen JD (2000) Minimum fuel neural networks and their applications to overcomplete signal representations. IEEE Trans Circuits Syst I 47(8):1146–1159

    Article  Google Scholar 

  • Xia YS (1996a) A new neural network for solving linear programming problems and its applications. IEEE Trans Neural Netw 7:525–529

    Article  PubMed  CAS  Google Scholar 

  • Xia YS (1996b) A new neural network for solving linear and quadratic programming problems. IEEE Trans Neural Netw 7:1544–1547

    Article  PubMed  CAS  Google Scholar 

  • Xia YS (1997) Neural network for solving extended linear programming. IEEE Trans Neural Netw 8:803–806

    Article  PubMed  CAS  Google Scholar 

  • Xia YS (2003) Global convergence analysis of Lagrangian networks. IEEE Trans Circuits Syst I vol 50

  • Xia YS (2004) An extended projection neural network for constrained optimization. Neural Comput 16:863–883

    Article  Google Scholar 

  • Xia YS, Feng G (2004) A modified neural network for quadratic programming with real-time applications. Neural Inf Process 3:69–76

    Google Scholar 

  • Xia YS, Feng G (2006) A neural network for robust LCMP beamforming. Signal Processing 86(10):2901–2912

    Google Scholar 

  • Xia YS, Kamel MS (2007a) Cooperative recurrent neural networks for the constrained L1 norm estimator. IEEE Trans Signal Process 55:3192–3205

    Article  Google Scholar 

  • Xia YS, Kamel MS (2007b) Novel cooperative neural fusion algorithms for image restoration. IEEE Trans Image Process 16:367–381

    Article  PubMed  Google Scholar 

  • Xia YS, Kamel MS (2007c) A measurement fusion method for nonlinear system identification and its cooperative learning algorithm. Neural Comput 19:1589–1632

    Article  PubMed  Google Scholar 

  • Xia YS, Kamel MS (2007d) Cooperative recurrent neural networks for the constrained L1 norm estimator. IEEE Trans Signal Process 55:3192–3205

    Article  Google Scholar 

  • Xia YS, Kamel MS (2008) A generalized least absolute deviation method for parameter estimation of autoregressive signals. IEEE Trans Neural Netw 19:107–118

    Article  PubMed  Google Scholar 

  • Xia YS, Wang JS (1995) Neural network for solving linear programming problems with bounded variables. IEEE Trans Neural Netw 6:515–519

    Article  PubMed  CAS  Google Scholar 

  • Xia YS, Wang J (1998a) A general methodology for designing globally convergent optimization neural networks. IEEE Trans Neural Netw 9:1331–1343

    Article  PubMed  CAS  Google Scholar 

  • Xia YS, Wang J (1998b) Neural network for solving the least absolute deviation fitting problem. Neurcomputing 19:13–21

    Article  CAS  Google Scholar 

  • Xia YS, Wang J (2001) A dual neural network for kinematic control of redundant robot manipulators. IEEE Trans Syst Man Cybern B 31(1):147–154

    Article  CAS  Google Scholar 

  • Xia YS, Wang J (2004a) A general projection neural network for solving monotone variational inequality and related optimization problems. IEEE Trans Neural Netw 15:318–328

    Article  PubMed  Google Scholar 

  • Xia Y, Wang J (2004b) A one-layer recurrent neural network for support vector machine learning. IEEE Trans Syst Man Cybern B 1261–1269

  • Xia YS, Wang J (2005) A recurrent neural network for solving nonlinear convex programs subject to linear constraints. IEEE Trans Neural Netw 16:379–386

    Article  PubMed  Google Scholar 

  • Xia YS, Leung H, Chan H (2006) A prediction fusion method for reconstructing spatial temporal dynamics using support vector machines. IEEE Trans Circuits Syst Ii-Express Briefs 53:62–66

    Article  Google Scholar 

  • Xia YS, Henry L, Wang J (2002a) A projection neural network and its application to constrained optimization problems. IEEE Trans Circuits Syst I 49(4):447–458

    Article  Google Scholar 

  • Xia YS, Henry L, Bossé E (2002b) Neural data fusion algorithms based on a linearly constrained least square method. IEEE Trans Neural Netw 13(2):320–329

    Article  PubMed  Google Scholar 

  • Xia Y, Feng G, Wang J (2004a) A Recurrent neural network with exponential convergence for solving convex quadratic program and related linear piecewise equations. Neural Netw 17:1003–1015

    Article  PubMed  Google Scholar 

  • Xia YS, Wang J, Fork LM (2004b) Grasping force optimization for multifingered robotic hands using a recurrent neural network. IEEE Trans Rob Autom 20:549–554

    Article  Google Scholar 

  • Xia YS, Feng G, Wang J (2005) A primal-dual neural network for on-line resolving constrained kinematic redundancy. IEEE Trans Syst Man Cybern B 35:54–64

    Article  CAS  Google Scholar 

  • Xia YS, Feng G, Kamel MS (2007) Development and analysis of neural dynamical approaches to solving nonlinear programming problems with application to optimal control. IEEE Trans Automat Contr, December

  • Yamaguchi S, Itakura H (1999) A modular neural network for control of mobile robots. Int Conf Neural Inform Processing 2:661–666

    Google Scholar 

  • Yang S, Browne A (2001) Neural network ensembles: combing multiple models for enhanced performance using a multistage approach. Expert Syst 21:279–288

    Article  Google Scholar 

  • Young PC (1970) An instrumental variable methods for real time identification of a noise process. Automatica 6:2711–287

    Article  Google Scholar 

  • Zervakis ME, Katsaggelos AK, Kwon TM (1995) A class of robust entropic functionals for image restoration. IEEE Trans Image Process 4:752–773

    Article  PubMed  CAS  Google Scholar 

  • Zhang GP (2000) Neural networks for classification: a survey. IEEE Trans Syst Man Cybern B 30:451–459

    Article  Google Scholar 

  • Zhang S, Constantinides AG (1992) Lagrange programming neural networks. IEEE Trans Circuits Syst 39(7):441–452

    Article  Google Scholar 

  • Zhang S, Zhu X, Zou L-H (1992) Second order neural networks for constrained optimization. IEEE Trans Neural Netw 3:1021–1024

    Article  PubMed  CAS  Google Scholar 

  • Zhang Y, Wang J, Xia YS (2003) A dual neural network for redundancy resolution of kinematically redundant manipulators subject to joint limits and joint velocity limits. IEEE Trans Neural Netw 14:658-667

    Article  PubMed  Google Scholar 

  • Zheng WX (1999) A least-squares based method for autoregressive signals in the presence of noise. IEEE Trans Circuits Syst Ii-Analog Digital Signal Process 46:81–85

    Article  Google Scholar 

  • Zheng WX (2000) Estimation of the parameters of autoregressive signals from colored noise-corrupted measurements. IEEE Signal Process Lett 7:201–204

    Article  Google Scholar 

  • Zooghby AHEl, Christodoulou CG, Georgiopoulos M (1998) Neural network-based adaptive beamforming for one- and two-dimensional antenna arrays. IEEE Trans Antennas Propagation 46:1891–1893

    Article  Google Scholar 

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Kamel, M.S., Xia, Y. Cooperative recurrent modular neural networks for constrained optimization: a survey of models and applications. Cogn Neurodyn 3, 47–81 (2009). https://doi.org/10.1007/s11571-008-9036-2

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