The objective of this paper is to present a modified structure and a training algorithm of the recurrent Elman neural network which makes it possible to explicitly take into account the time-delay of the process and a Model Predictive Control (MPC) algorithm for such a network. In MPC the predicted output trajectory is repeatedly linearized on-line along the future input trajectory, which leads to a quadratic optimization problem, nonlinear optimization is not necessary. A strongly nonlinear benchmark process (a simulated neutralization reactor) is considered to show advantages of the modified Elman neural network and the discussed MPC algorithm. The modified neural model is more precise and has a lower number of parameters in comparison with the classical Elman structure. The discussed MPC algorithm with on-line linearization gives similar trajectories as MPC with nonlinear optimization repeated at each sampling instant.
 R. BONNEAU, M. T. FACCIOTTI, D. J. REISS, A. K. SCHMID, M. PAN, A. KAUR, V. THORSSON, P. SHANNON, M. H. JOHNSON, J. C. BARE, W. LONGABAUGH, M. VUTHOORI, K. WHITEHEAD, A. MADAR, L. SUZUKI, T. MORI, D. E CHANG, J. DIRUGGIERO, C. H. JOHNSON, L. HOOD and N. S. BALIGA: A predictive model for transcriptional control of physiology in a free living cell. Cell, 131(7), (2007), 1354-1365.
 E. F. CAMACHO and C. BORDONS: Model Predictive Control. Springer, London, 1999.
 X. CHEN, J. CHEN and B. LEI: Identification of pH neutralization process based on the T-S fuzzy model, 215 CCIS of Communications in Computer and Information Science. Springer, Berlin, Heidelberg, 2011.
 F. DECLERCQ and R. DE KEYSER: Comparative study of neural predictors in model based predictive control. In Proc. of Int. Workshop on Neural Networks for Identification, Control, Robotics, and Signal/Image Processing, (1996), 20-28.
 J. L. ELMAN: Finding structure in time. Cognitive Science, 14(2), (1990), 179-211.
 J. C. GÓMEZ and E. BAEYENS: Subspace-based identification algorithms for hammerstein and wiener models. European J. of Control, 11(2), (2005), 127-136.
 J. C. GÓMEZ, A. JUTAN and E. BAEYENS: Wiener model identification and predictive control of a ph neutralisation process. IEE Proceedings: Control Theory and Applications, 151(3), (2004), 329-338.
 K. A. GREENE, K. W. BAUER JR., M. KABRISKY, S. K. ROGERS and G. F. WILSON: Estimating pilot workload using Elman recurrent neural networks: a preliminary investigation. In Intelligent Engineering Systems Through Artificial Neural Networks, 7 (1997), 703-708.
 M. T. HAGAN, H. B. DEMUTH, MARK BEALE and O. DE JESUS: Neural Network Design. PWS Publishing Co, Boston, MA, USA, 1996.
 B. HAN and M. HAN: Nonlinear time delay systems identification based on dynamic bp algorithm. Dalian Ligong Daxue Xuebao/Journal of Dalian University of Technology, 50(5), (2010), 777-781.
 S. HAYKIN: Neural Networks: A Comprehensive Foundation. Prentice Hall PTR, Upper Saddle River, NJ, USA, 2nd edition, 1998.
 R. HOVORKA, V. CANONICO, L. J. CHASSIN, U. HAUETER, M. MASSIBENEDETTI, M. O. FEDERICI, T. R. PIEBER, H. C. SCHALLER, L. SCHAUPP, T. VERING and M. E. WILINSKA: Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes. Physiological Measurement, 25(4), (2004), 905-920.
 Y. JIA, L. Y ZHANG and T. Y CHAI: Based on fuzzy adaptive control of model predictive in slurry neutralization process. Dongbei Daxue Xuebao/Journal of Northeastern University, 35(5), (2014), 617-621.
 M. ŁAWRYŃCZUK: Accuracy and computational efficiency of suboptimal nonlinear predictive control based on neural models. Applied Soft Computing J., 11(2), (2011), 2202-2215.
 M. ŁAWRYŃCZUK: Practical nonlinear predictive control algorithms for neural wiener models. J. of Process Control, 23(5), (2013), 696-714.
 M. ŁAWRYŃCZUK: Computationally Efficient Model Predictive Control Algorithms. Springer, 2014.
 P. LI, Y. LI, Q. XIONG, Y. CHAI and Y. ZHANG: Application of a hybrid quantized Elman neural network in short-term load forecasting. Int. J. of Electrical Power and Energy Systems, 55 (2014), 749-759.
 Q. LI, Y. QIN, Z.Y. WANG, Z.X. ZHAO, M.H. ZHAN and Y. LIU: Prediction of urban rail transit sectional passenger flow based on elman neural network. Applied Mechanics and Materials, 505-506 (2014), 1023-1027.
 J. W LIOU, W. C CHENG, J. C HUANG and C. Y LIOU: Distributed representation of word by using Elman network. Int. J. of Intelligent Information and Database Systems, 7(4), (2013), 373-386.
 J. M. MACIEJOWSKI: Predictive Control with Constraints. Prentice Hall, Harlow, 2002.
 D. P. MANDIC and J. CHAMBERS: Recurrent Neural Networks for Prediction: Learning Algorithms,Architectures and Stability. John Wiley & Sons, Inc, New York, NY, USA, 2001.
 A. MARCINIAK and J. KORBICZ: Modular Neural Networks pages 135-177. Biocybernetyka i in˙zynieria biomedyczna 2000. 6 Sieci neuronowe, ISBN: 83-87674-18-4. Akademicka Oficyna Wydaw. EXIT, Warszawa, 2000, (in Polish).
 J. M. ZAMARRE NO and P. VEGA: State-space neural network. properties and application. Neural Networks, 11(6), (1998), 1099-1112.
 J. NOCEDAL and S.J. WRIGHT: Numerical Optimization. Springer, Berlin, New York, 2006.
 S. OSOWSKI: Neural Networks for Information Processing. Oficyna Wydawnicza Politechniki Warszawskiej, Warszawa, 2006, (in Polish).
 P. PLAWIAK and R. TADEUSIEWICZ: Approximation of phenol concentration using novel hybrid computational intelligence methods. Int. J. of Applied Mathematics and Computer Science, 24(1), (2014), 165-181.
 S. J. QIN and T. BADGWELL: A survey of industrial model predictive control technology. Control Engineering Practice, 11(7), (2003), 733-764.
 D. SAMEK: Elman neural networks in model predictive control. In Proc. of the 23rd European Conf. on Modelling and Simulation, (2009), 577-581.
 S. SEKER, E. AYAZ and E. TÜRKCAN: Elman’s recurrent neural network applications to condition monitoring in nuclear power plant and rotating machinery. Engineering Applications of Artificial Intelligence, 16(7-8), (2003), 647-656.
 P. TATJEWSKI: Advanced Control of Industrial Processes, Structures and Algorithms. Springer, London, 2007.
 J. G WU and H. LUNDSTEDT: Prediction of geomagnetic storms from solar wind data using Elman recurrent neural networks. Geophysical Research Letters, 23(4), (1996), 319-322.
 C. XIA, X. XIANG, B. LEI and D. PENG: Research on a dynamic recurrent Elman neural network model for electric load forecasting and its wilcoxon test. J. of Computational Information Systems, 6(3), (2010), 959-966.
 J. XU and M. ZHANG: Neural network modeling and generalized predictive control for an autonomous underwater vehicle. In 6th IEEE Int. Conf. on Industrial Informatics, (2008), 487-491.
 C. ZHOU, L. Y. DING and R. HE: Pso-based Elman neural network model for predictive control of air chamber pressure in slurry shield tunneling under yangtze river. Automation in Construction, 36 (2013), 208-217.