Nonlinear predictive control based on neural multi-models

Ławryńczuk, Maciej; Tatjewski, Piotr

doi:10.2478/v10006-010-0001-y

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.

References

Åkesson, B. M. and Toivonen, H. T. (2006). A neural network model predictive controller, Journal of Process Control 16(3): 937-946.10.1016/j.jprocont.2006.06.001
Search in Google Scholar
Alexandridis, A. and Sarimveis, H. (2005). Nonlinear adaptive model predictive control based on self-correcting neural network models, AIChE Journal 51(9): 2495-2506.10.1002/aic.10505
Search in Google Scholar
Bazaraa, M. S., Sherali, J. and Shetty, K. (1993). Nonlinear Programming: Theory and Algorithms, John Wiley & Sons, New York, NY.
Search in Google Scholar
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): 201-215.10.1016/j.engappai.2008.06.001
Search in Google Scholar
Doyle, F. J., Ogunnaike, B. A. and Pearson, R. K. (1995). Nonlinear model-based control using second-order Volterra models, Automatica 31(5): 697-714.10.1016/0005-1098(94)00150-H
Search in Google Scholar
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): 345-356.10.1016/j.compag.2005.08.005
Search in Google Scholar
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): 681-700.10.1016/0005-1098(84)90018-9
Search in Google Scholar
Haykin, S. (1999). Neural Networks. A Comprehensive Foundation, 2nd Edition, Prentice-Hall, Englewood Cliffs, NJ.
Search in Google Scholar
Henson, M. A. (1998). Nonlinear model predictive control: Current status and future directions, Computers and Chemical Engineering 23(2): 187-202.10.1016/S0098-1354(98)00260-9
Search in Google Scholar
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/v10006-007-0020-5.10.2478/v10006-007-0020-5
Search in Google Scholar
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.
Search in Google Scholar
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.
Search in Google Scholar
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/v10006-009-0019-1.10.2478/v10006-009-0019-1
Search in Google Scholar
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.
Search in Google Scholar
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).10.1016/S1474-6670(17)57157-8
Search in Google Scholar
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): 1366-1375.10.1109/TIE.2007.896492
Search in Google Scholar
Luyben, W. L. (1990). Process Modelling, Simulation and Control for Chemical Engineers, McGraw Hill, New York, NY.
Search in Google Scholar
Maciejowski, J. M. (2002). Predictive Control with Constraints, Prentice Hall, Harlow.
Search in Google Scholar
Morari, M. and Lee, J. (1999). Model predictive control: Past, present and future, Computers and Chemical Engineering 23(4): 667-682.10.1016/S0098-1354(98)00301-9
Search in Google Scholar
Narendra, K. S. and Parthasarathy, K. (1990). Identification and control of dynamical systems using neural networks, IEEE Transactions on Neural Networks 1(1): 4-26.10.1109/72.80202
Search in Google Scholar
Nørgaard, M., Ravn, O., Poulsen, N. K. and Hansen, L. K. (2000). Neural Networks for Modelling and Control of Dynamic Systems, Springer, London.10.1007/978-1-4471-0453-7
Search in Google Scholar
Parisini, T., Sanguineti, M. and Zoppoli, R. (1998). Nonlinear stabilization by receding-horizon neural regulators, International Journal of Control 70(3): 341-362.10.1080/002071798222271
Search in Google Scholar
Pearson, R. K. (2003). Selecting nonlinear model structures for computer control, Journal of Process Control 13(1): 1-26.10.1016/S0959-1524(02)00022-7
Search in Google Scholar
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): 1-9.10.1016/j.engappai.2006.05.012
Search in Google Scholar
Qin, S. J. and Badgwell, T. (2003). A survey of industrial model predictive control technology, Control Engineering Practice 11(7): 733-764.10.1016/S0967-0661(02)00186-7
Search in Google Scholar
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): 122-130.10.1109/72.10542518276413
Search in Google Scholar
Rossiter, J. A. and Kouvaritakis, B. (2001). Modelling and implicit modelling for predictive control, International Journal of Control 74(11): 1085-1095.10.1080/00207170110054129
Search in Google Scholar
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): 1338-1352.10.1021/ie00005a014
Search in Google Scholar
Tatjewski, P. (2007). Advanced Control of Industrial Processes, Structures and Algorithms, Springer, London.
Search in Google Scholar
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.
Search in Google Scholar
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): 19-27.10.1016/0959-1524(95)95942-7
Search in Google Scholar

Nonlinear predictive control based on neural multi-models

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