Modelling Chaos with Neural Networks

  • R. Baratti
  • B. Cannas
  • A. Fanni
  • S. Tronci
Conference paper


In this work, a comparison between alternative neural approaches to model chaotic systems is reported. In particular, two different approaches have been presented. The first, is a Locally Recurrent Neural Network that, keeping the feedforward architecture of the MLP, replaces the classical synapses with Finite Impulse Response and Infinite Impulse Response filters. The second, is a novel dynamic neural network obtained by making recurrent the neurons in the output layer. The performances of the proposed approaches have been tested on the problem of modeling the dynamics of a non-isothermal, continuously stirred tank reactor when two consecutive first order reactions lead to a chaotic behavior. Moreover, the obtained dynamic neural networks have been used to develop a Generic Model Control controller.


Neural Network Hide Layer Finite Impulse Response Model Predictive Control Recurrent Neural Network 
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  1. Garcia C.E., Morari M. (1982) Internal Model Control: 1. A Unifying Review and Some New Results. Ind. Eng. Chem. Process Des. Dev., 21, 308–321CrossRefGoogle Scholar
  2. Henson M.A. (1998) Nonlinear Model Predictive Control: Current Status and Future Directions. Comp. Chem. Eng., 23, 187–202CrossRefGoogle Scholar
  3. Yu Y., Nikolaou M. (1993) Dynamic Process Modeling with Recurrent Neural Networks. AIChE J., 39, 1654–1667CrossRefGoogle Scholar
  4. Nikolaou, Hanagnandi M.V. (1993) Control of Nonlinear Dynamical Systems Modeled by Recurrent Neural Networks. AIChE J., 39, 1890–1894CrossRefGoogle Scholar
  5. Turner P., Montague G., Morris J. (1996) Dynamic Neural Networks in Nonlinear Predictive Control (An Industrial Application). Comp. Chem. Eng., 20, 937–942CrossRefGoogle Scholar
  6. Scott G.M., Ray W.H. (1993) Creating efficient nonlinear neural network process models that allow model interpretation. J. Proc. Cont., 3, 163–178CrossRefGoogle Scholar
  7. Shaw A.M., Doyle III F.J., Schwaber J.S. (1997) A Dynamic Neural Network Approach to Nonlinear Process Modeling. Comp. Chem. Eng., 21, 371–385CrossRefGoogle Scholar
  8. Shaw A.M., Doyle III F.J. (1997) Multivariate Nonlinear Control Applications for a High Purity Distillation Column Using a Recurrent Dynamic Neuron Model. J. Proc. Cont., 7, 255–268CrossRefGoogle Scholar
  9. Back D., Tsoi A.C. (1991) FIR and IIR synapses, a new neural network architecture for time series modelling. Neural Computation, 3, 375–385, Massachusetts Institute of TechnologyGoogle Scholar
  10. Back D., Tsoi A.C. (1993) A simplified gradient algorithm for IIR synapse multilayer perceptrons. Neural Computation, 5, 456–462, Massachusetts Institute of TechnologyCrossRefGoogle Scholar
  11. Wan E.A. (1990) Temporal backpropagation for FIR neural networks, Proceedings of International Joint Conference on Neural Networks, San Diego, June 1990, 575–580Google Scholar
  12. Khotanzad R., Lu Afkhami-Rohani T., Abaye A., Davis M., Maratukulam D.J. (1997) ANNSTLF- A neural-network-based electric load forecasting system. IEEE Trans, on Neural Networks, 8Google Scholar
  13. Cannas B., Celli G., Marchesi M., Pilo F. (1998) Neural Networks for Power System Condition Monitoring and Protection. Neurocomputing, 23, 111–123CrossRefGoogle Scholar
  14. Celli G., Marchesi M., Mocci F., Pilo F. (1997) Applications of neural networks in power distribution systems diagnosis and control. Proc. 32nd Universities Power Engineering Conference UPEC ’97, Manchester (UK), 10–12 Sept. 1997, 523–526Google Scholar
  15. Celli G., Pilo F., Sannais R., Tosi M. (1998) Voltage quality improvement by Custom Power devices: applications of Solid-State Breakers and Neural Controllers. Proc. of SPEEDAM 98 Conference, Sorrento (ITALY), 3–5 June 1998Google Scholar
  16. Cannas B., Cincotti S., Fanni A., Marchesi M., Pilo F., Usai M. (1998) Performance analysis of locally recurrent neural networks. COMPEL — International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 17, 5 /6, 708–716CrossRefGoogle Scholar
  17. Baratti R., Servida A. (1999) DMC control strategy for a CSTR based on dynamic neural model. Proc. of Ichea P-4, Forth Italian Conference on Chemical Eng., Florence, Italy, May 2–5 1999, 179–182Google Scholar
  18. Chemburkar R.M., Rossler O.E., Varma A. (1987) Dynamics of consecutive reactions in a CSTR — case study. Chemical Eng. Sci., 42, 1507–1509CrossRefGoogle Scholar
  19. Ott E., Grebogi C., Yorke J.A. (1990) Controlling Chaos, Physical Rev. Letters, 64, 1196–1199CrossRefGoogle Scholar
  20. Campolucci P., Uncini A., Piazza F., Rao B.D. (1999) On-line learning algorithms for locally recurrent neural networks. IEEE Trans, on Neural Networks, 10, 253–271CrossRefGoogle Scholar
  21. Werbos P. (1990) Backpropagation through time: what it does and how to do it. Proc. IEEE, Special Issue on Neural Networks, 2, 1550–1560Google Scholar
  22. Ogunnaike B.A., Ray W.H. (1994) Process Dynamics, Modeling, and Control. Oxford University Press, OxfordGoogle Scholar
  23. Baratti R., Cannas B., Fanni A., Pilo F. (2000) Automated Recurrent Neural Network Design to Model the Dynamics of Complex System. Neural Computing & Applications, 9, 190–201CrossRefGoogle Scholar
  24. Glover F. (1989) Tabu search — part. I. ORSA Journal on Computing, 1, 190–206Google Scholar
  25. Glover F. (1990) Tabu search — part. II. ORSA Journal on Computing, 2, 4–32Google Scholar
  26. Henon M. (1982) On the Numerical Computation of Poincaré Maps. Physica 5D, 412–414Google Scholar

Copyright information

© Springer-Verlag Italia, Milan 2002

Authors and Affiliations

  • R. Baratti
    • 1
    • 2
  • B. Cannas
    • 1
    • 2
  • A. Fanni
    • 1
    • 2
  • S. Tronci
    • 1
    • 2
  1. 1.Dipartimento di Ingegneria Chimica e Scienza dei MaterialiUniversità di CagliariCagliariItaly
  2. 2.Dipartimento di Ingegneria Elettrica ed ElettronicaUniversità di CagliariCagliariItaly

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