Recursive lazy learning for modeling and control

  • Gianluca Bontempi
  • Mauro Birattari
  • Hugues Bersini
Instance Based Learning
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1398)


This paper presents a local method for modeling and control of non-linear dynamical systems from input-output data. The proposed methodology couples a local model identification inspired by the lazy learning technique, with a control strategy based on linear optimal control theory. The local modeling procedure uses a query-based approach to select the best model configuration by assessing and comparing different alternatives. A new recursive technique for local model identification and validation is presented, together with an enhanced statistical method for model selection. The control method combines the linearization provided by the local learning techniques with optimal linear control theory, to control non-linear systems in configurations which are far from equilibrium. Simulations of the identification of a non-linear benchmark model and of the control of a complex non-linear system (the bioreactor) are presented. The experimental results show that the approach can obtain better performance than neural networks in identification and control, even using smaller training data sets.


Near Neighbor Query Point Optimal Control Theory Linearize Quadratic Regulator Local Learning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    D.W. Aha. Incremental, instance-based learning of independent and graded concept descriptions. In Sixth International Machine Learning Workshop, pages 387–391, San Mateo CA, 1989. Morgan Kaufmann.Google Scholar
  2. 2.
    C. G. Atkeson. Using local optimizers to speed up global optimization in dynamic programming. In J. D. Cowan, G. Tesauro, and J. Alspector, editors, Advances in Neural Information Processing Systems 6, pages 663–670. Morgan Kaufmann, 1994.Google Scholar
  3. 3.
    C.G. Atkeson, A.W. Moore, and S. Schaal. Locally weighted learning. Artificial Intelligence Review, 11(1-5):11–73, 1997.CrossRefGoogle Scholar
  4. 4.
    C.G. Atkeson, A.W. Moore, and S. Schaal. Locally weighted learning for control. Artificial Intelligence Review, 11(1-5):75–113, 1997.CrossRefGoogle Scholar
  5. 5.
    J.K. Benedetti. On the non parametric estimation of regression functions. Journal of the Royal Statistical Society, Series B, (39):248–253, 1977.Google Scholar
  6. 6.
    H. Bersini, M. Birattari, and G. Bontempi. Adaptive memory-based regression methods. In Proceedings of the 1998 IEEE International Joint Conference on Neural Networks, 1998. to appear.Google Scholar
  7. 7.
    H. Bersini and V. Gorrini. A simplification of the back-propagation-through-time algorithm for optimal neurocontrol. IEEE Trans. on Neural Networks, 8(2):437–441, 1997.CrossRefGoogle Scholar
  8. 8.
    L. Bottou and V.N. Vapnik. Local learning algorithms. Neural Computation, 4(6):888–900, 1992.Google Scholar
  9. 9.
    D.W. Clarke. Advances in Model-Based Predictive Control. Oxford University Press, 1994.Google Scholar
  10. 10.
    P.R. Cohen. Empirical Methods for Artificial Intelligence. The MIT Press, Cambridge, MA, 1995.Google Scholar
  11. 11.
    B. V. Dasarathy. Nearest neighbor (NN) norms: NN pattern classification techniques. IEEE Computer Society Press, 1991.Google Scholar
  12. 12.
    B. Efron and R.J. Tibshirani. An Introduction to the Bootstrap. Chapman and Hall, New York, NY, 1993.Google Scholar
  13. 13.
    V.A. Epanechnikov. Non parametric estimation of a multivariate probability density. Theory of Probability and Its Applications, (14):153–158, 1969.Google Scholar
  14. 14.
    A.A. Fel'dbaum. Optimal control systems. Academic Press, New York, NY, 1965.Google Scholar
  15. 15.
    G.C. Goodwin and K. S. Sin. Adaptive Filtering Prediction and Control. Prentice-Hall, 1984.Google Scholar
  16. 16.
    D. Jacobson and D. Mayne. Differential Dynamic Programming. Elsevier Sci. Publ., New York, 1970.Google Scholar
  17. 17.
    T.A. Johansen and B.A. Foss. Constructing narmax models using armax models. International Journal of Control, 58:1125–1153, 1993.MathSciNetGoogle Scholar
  18. 18.
    I.J. Leontaritis and S.A. Billings. Input-output parametric models for non-linear systems. International Journal of Control, 41(2):303–344, 1985.Google Scholar
  19. 19.
    W.T. MillerIII, R.S. Sutton, and P.J. Werbos, editors. Neural Networks for Control. The MIT Press, 1990.Google Scholar
  20. 20.
    R. Murray-Smith and T.A. Johansen, editors. Multiple Model Approaches to Modelling and Control. Taylor and Francis, 1997.Google Scholar
  21. 21.
    R.H. Myers. Classical and Modern Regression with Applications. PWS-KENT, Boston, MA, 1990.Google Scholar
  22. 22.
    K.S. Narendra and S.M. Li. Neural networks in control systems. In M.C. Mozer Paul Smolensky and D.E. Rumelhart, editors, Mathematical Perspectives on Neural Networks, chapter 11, pages 347–394. Lawrence Erlbaum Associates, 1996.Google Scholar
  23. 23.
    J.S. Shamma and M. Athans. Gain scheduling: Potential hazards and possible remedies. IEEE Control Systems Magazine, pages 101–107, June 1992.Google Scholar
  24. 24.
    S. Siegel and Jr. N.J. Castellan.Non Parametric Statistics for the Behavioral Sciences. McGraw-Hill International, 2nd edition, 1988.Google Scholar
  25. 25.
    R.F. Stengel. Stochastic optimal control: theory and application. John Wiley and Sons, New York, NY, 1986.Google Scholar
  26. 26.
    T. Takagi and M. Sugeno. Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on System, Man and Cybernetics, 15(1):116–132, 1985.Google Scholar
  27. 27.
    K. Tanaka. Stability and stabilizability of fuzzy-neural-linear control systems. IEEE Transactions on Fuzzy Systems, 3(4):438–447, November 1995.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Gianluca Bontempi
    • 1
  • Mauro Birattari
    • 1
  • Hugues Bersini
    • 1
  1. 1.Iridia - CP 194/6 Université Libre de Bruxelles 50BruxellesBelgium

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