Skip to main content
  • 242 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Garcia C.E., Morari M. (1982) Internal Model Control: 1. A Unifying Review and Some New Results. Ind. Eng. Chem. Process Des. Dev., 21, 308–321

    Article  CAS  Google Scholar 

  • Henson M.A. (1998) Nonlinear Model Predictive Control: Current Status and Future Directions. Comp. Chem. Eng., 23, 187–202

    Article  CAS  Google Scholar 

  • Yu Y., Nikolaou M. (1993) Dynamic Process Modeling with Recurrent Neural Networks. AIChE J., 39, 1654–1667

    Article  Google Scholar 

  • Nikolaou, Hanagnandi M.V. (1993) Control of Nonlinear Dynamical Systems Modeled by Recurrent Neural Networks. AIChE J., 39, 1890–1894

    Article  Google Scholar 

  • Turner P., Montague G., Morris J. (1996) Dynamic Neural Networks in Nonlinear Predictive Control (An Industrial Application). Comp. Chem. Eng., 20, 937–942

    Article  Google Scholar 

  • Scott G.M., Ray W.H. (1993) Creating efficient nonlinear neural network process models that allow model interpretation. J. Proc. Cont., 3, 163–178

    Article  CAS  Google Scholar 

  • Shaw A.M., Doyle III F.J., Schwaber J.S. (1997) A Dynamic Neural Network Approach to Nonlinear Process Modeling. Comp. Chem. Eng., 21, 371–385

    Article  CAS  Google Scholar 

  • 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, 255–268

    Article  CAS  Google Scholar 

  • 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 Technology

    Google Scholar 

  • Back D., Tsoi A.C. (1993) A simplified gradient algorithm for IIR synapse multilayer perceptrons. Neural Computation, 5, 456–462, Massachusetts Institute of Technology

    Article  Google Scholar 

  • Wan E.A. (1990) Temporal backpropagation for FIR neural networks, Proceedings of International Joint Conference on Neural Networks, San Diego, June 1990, 575–580

    Google Scholar 

  • 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, 8

    Google Scholar 

  • Cannas B., Celli G., Marchesi M., Pilo F. (1998) Neural Networks for Power System Condition Monitoring and Protection. Neurocomputing, 23, 111–123

    Article  Google Scholar 

  • 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, 523–526

    Google Scholar 

  • 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 1998

    Google Scholar 

  • 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, 708–716

    Article  Google Scholar 

  • 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, 179–182

    Google Scholar 

  • Chemburkar R.M., Rossler O.E., Varma A. (1987) Dynamics of consecutive reactions in a CSTR — case study. Chemical Eng. Sci., 42, 1507–1509

    Article  CAS  Google Scholar 

  • Ott E., Grebogi C., Yorke J.A. (1990) Controlling Chaos, Physical Rev. Letters, 64, 1196–1199

    Article  Google Scholar 

  • 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, 253–271

    Article  CAS  Google Scholar 

  • Werbos P. (1990) Backpropagation through time: what it does and how to do it. Proc. IEEE, Special Issue on Neural Networks, 2, 1550–1560

    Google Scholar 

  • Ogunnaike B.A., Ray W.H. (1994) Process Dynamics, Modeling, and Control. Oxford University Press, Oxford

    Google Scholar 

  • 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, 190–201

    Article  Google Scholar 

  • Glover F. (1989) Tabu search — part. I. ORSA Journal on Computing, 1, 190–206

    Google Scholar 

  • Glover F. (1990) Tabu search — part. II. ORSA Journal on Computing, 2, 4–32

    Google Scholar 

  • Henon M. (1982) On the Numerical Computation of Poincaré Maps. Physica 5D, 412–414

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Italia, Milan

About this paper

Cite this paper

Baratti, R., Cannas, B., Fanni, A., Tronci, S. (2002). Modelling Chaos with Neural Networks. In: Continillo, G., Giona, M., Crescitelli, S. (eds) Nonlinear Dynamics and Control in Process Engineering — Recent Advances. Springer, Milano. https://doi.org/10.1007/978-88-470-2208-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-88-470-2208-9_4

  • Publisher Name: Springer, Milano

  • Print ISBN: 978-88-470-0161-9

  • Online ISBN: 978-88-470-2208-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics