# Nonlinear predictive control based on neural multi-models

Maciej Ławryńczuk; Piotr Tatjewski

International Journal of Applied Mathematics and Computer Science (2010)

- Volume: 20, Issue: 1, page 7-21
- ISSN: 1641-876X

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topMaciej Ławryńczuk, and Piotr Tatjewski. "Nonlinear predictive control based on neural multi-models." International Journal of Applied Mathematics and Computer Science 20.1 (2010): 7-21. <http://eudml.org/doc/207979>.

@article{MaciejŁawryńczuk2010,

abstract = {This paper discusses neural multi-models based on Multi Layer Perceptron (MLP) networks and a computationally efficient nonlinear Model Predictive Control (MPC) algorithm which uses such models. Thanks to the nature of the model it calculates future predictions without using previous predictions. This means that, unlike the classical Nonlinear Auto Regressive with eXternal input (NARX) model, the multi-model is not used recurrently in MPC, and the prediction error is not propagated. In order to avoid nonlinear optimisation, in the discussed suboptimal MPC algorithm the neural multi-model is linearised on-line and, as a result, the future control policy is found by solving of a quadratic programming problem.},

author = {Maciej Ławryńczuk, Piotr Tatjewski},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {process control; model predictive control; neural networks; optimisation; linearisation},

language = {eng},

number = {1},

pages = {7-21},

title = {Nonlinear predictive control based on neural multi-models},

url = {http://eudml.org/doc/207979},

volume = {20},

year = {2010},

}

TY - JOUR

AU - Maciej Ławryńczuk

AU - Piotr Tatjewski

TI - Nonlinear predictive control based on neural multi-models

JO - International Journal of Applied Mathematics and Computer Science

PY - 2010

VL - 20

IS - 1

SP - 7

EP - 21

AB - This paper discusses neural multi-models based on Multi Layer Perceptron (MLP) networks and a computationally efficient nonlinear Model Predictive Control (MPC) algorithm which uses such models. Thanks to the nature of the model it calculates future predictions without using previous predictions. This means that, unlike the classical Nonlinear Auto Regressive with eXternal input (NARX) model, the multi-model is not used recurrently in MPC, and the prediction error is not propagated. In order to avoid nonlinear optimisation, in the discussed suboptimal MPC algorithm the neural multi-model is linearised on-line and, as a result, the future control policy is found by solving of a quadratic programming problem.

LA - eng

KW - process control; model predictive control; neural networks; optimisation; linearisation

UR - http://eudml.org/doc/207979

ER -

## References

top- Åkesson, B. M. and Toivonen, H. T. (2006). A neural network model predictive controller, Journal of Process Control 16(3): 937-946.
- Alexandridis, A. and Sarimveis, H. (2005). Nonlinear adaptive model predictive control based on self-correcting neural network models, AIChE Journal 51(9): 2495-2506.
- Bazaraa, M. S., Sherali, J. and Shetty, K. (1993). Nonlinear Programming: Theory and Algorithms, John Wiley & Sons, New York, NY. Zbl0774.90075
- da Cruz Meleiro, L. A., José, F., Zuben, V. and Filho, R. M. (2009). Constructive learning neural network applied to identification and control of a fuel-ethanol fermentation process, Engineering Applications of Artificial Intelligence 22(2): 201-215.
- Doyle, F. J., Ogunnaike, B. A. and Pearson, R. K. (1995). Nonlinear model-based control using second-order Volterra models, Automatica 31(5): 697-714. Zbl0823.93022
- El Ghoumari, M. Y. and Tantau, H. J. (2005). Non-linear constrained MPC: Real-time implementation of greenhouse air temperature control, Computers and Electronics in Agriculture 49(3): 345-356.
- Greco, C., Menga, G., Mosca, E. and Zappa, G. (1984). Performance improvement of self tuning controllers by multistep horizons: The MUSMAR approach, Automatica 20(5): 681-700. Zbl0577.93039
- Haykin, S. (1999). Neural Networks. A Comprehensive Foundation, 2nd Edition, Prentice-Hall, Englewood Cliffs, NJ. Zbl0934.68076
- Henson, M. A. (1998). Nonlinear model predictive control: Current status and future directions, Computers and Chemical Engineering 23(2): 187-202.
- Ławryńczuk, M. (2007). A family of model predictive control algorithms with artificial neural networks, International Journal of Applied Mathematics and Computer Science 17(2): 217-232, DOI: 10.2478/v10006-007-0020-5. Zbl1119.93350
- Ławryńczuk, M. (2008). Suboptimal nonlinear predictive control with neural multi-models, in L. Rutkowski, R. Tadeusiewicz, L. A. Zadeh and J. Zurada (Eds), The 9th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2008, Zakopane, Poland (Computational Intelligence: Methods and Applications), Exit, Warsaw, pp. 45-56. Zbl1169.93375
- Ławryńczuk, M. (2009a). Computationally efficient nonlinear predictive control based on RBF neural multi-models, in M. Kolehmainen, P. Toivanen and B. Beliczyński (Eds), The Ninth International Conference on Adaptive and Natural Computing Algorithms, ICANNGA 2009, Kuopio, Finland, Lecture Notes in Computer Science, Vol. 5495, Springer, Heidelberg, pp. 89-98.
- Ławryńczuk, M. (2009b). Efficient nonlinear predictive control based on structured neural models, International Journal of Applied Mathematics and Computer Science 19(2): 233-246, DOI: 10.2478/v10006-009-0019-1. Zbl1167.93337
- LeCun, Y., Denker, J. and Solla, S. (1990). Optimal brain damage, in D. Touretzky (Ed.), Advances of NIPS2, Morgan Kaufmann, San Mateo, CA, pp. 598-605.
- Liu, D., Shah, S. L. and Fisher, D. G. (1999). Multiple prediction models for long range predictive control, Proceedings of the IFAC World Congress, Beijing, China, (on CD-ROM).
- Lu, C. H. and Tsai, C. C. (2008). Adaptive predictive control with recurrent neural network for industrial processes: An application to temperature control of a variable-frequency oil-cooling machine, IEEE Transactions on Industrial Electronics 55(3): 1366-1375.
- Luyben, W. L. (1990). Process Modelling, Simulation and Control for Chemical Engineers, McGraw Hill, New York, NY.
- Maciejowski, J. M. (2002). Predictive Control with Constraints, Prentice Hall, Harlow. Zbl0978.93002
- Morari, M. and Lee, J. (1999). Model predictive control: Past, present and future, Computers and Chemical Engineering 23(4): 667-682.
- Narendra, K. S. and Parthasarathy, K. (1990). Identification and control of dynamical systems using neural networks, IEEE Transactions on Neural Networks 1(1): 4-26.
- Nørgaard, M., Ravn, O., Poulsen, N. K. and Hansen, L. K. (2000). Neural Networks for Modelling and Control of Dynamic Systems, Springer, London. Zbl0953.93003
- Parisini, T., Sanguineti, M. and Zoppoli, R. (1998). Nonlinear stabilization by receding-horizon neural regulators, International Journal of Control 70(3): 341-362. Zbl0925.93823
- Pearson, R. K. (2003). Selecting nonlinear model structures for computer control, Journal of Process Control 13(1): 1-26.
- Peng, H., Yang, Z. J., Gui, W., Wu, M., Shioya, H. and Nakano, K. (2007). Nonlinear system modeling and robust predictive control based on RBF-ARX model, Engineering Applications of Artificial Intelligence 20(1): 1-9.
- Qin, S. J. and Badgwell, T. (2003). A survey of industrial model predictive control technology, Control Engineering Practice 11(7): 733-764.
- Qin, S. Z., Su, H. T. and McAvoy, T. J. (1992). Comparison of four neural net learning methods for dynamic system identification, IEEE Transactions on Neural Networks 3(1): 122-130.
- Rossiter, J. A. and Kouvaritakis, B. (2001). Modelling and implicit modelling for predictive control, International Journal of Control 74(11): 1085-1095. Zbl1015.93020
- Su, H. T. and McAvoy, T. J. (1992). Long-term predictions of chemical processes using recurrent neural networks: A parallel training approach, Industrial and Engineering Chemistry Research 31(5): 1338-1352.
- Tatjewski, P. (2007). Advanced Control of Industrial Processes, Structures and Algorithms, Springer, London. Zbl1134.93037
- Tatjewski, P. and Ławryńczuk, M. (2006). Soft computing in model-based predictive control, International Journal of Applied Mathematics and Computer Science 16(1): 101-120. Zbl1334.93068
- Temeng, K. O., Schnelle, P. D. and McAvoy, T. J. (1995). Model predictive control of an industrial packed bed reactor using neural networks, Journal of Process Control 5(1): 19-27.

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