Nonlinear Robust Identification with ε – GA: FPS Under Several Norms Simultaneously

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3512)


In nonlinear robust identification context, a process model is represented by a nominal model and possible deviations. With parametric models this process model can be expressed as the so-called Feasible Parameter Set (FPS), which derives from the minimization of identification error specific norms. In this work, several norms are used simultaneously to obtain the FPS. This fact improves the model quality but, as counterpart, it increases the optimization problem complexity resulting in a multimodal problem with an infinite number of minima with the same value which constitutes FPS contour. A special Evolutionary Algorithm (ε– GA) has been developed to find this contour. Finally, an application to a thermal process identification is presented.


Multiobjective Optimization Optimization Problem Complexity Multimodal Problem IFAC Symposium Transfer Function Estimation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Coello, C., Veldhuizen, D., Lamont, G.: Evolutionary algorithms for solving multi-objective problems. Kluwer Academic Publishers, Dordrecht (2002)zbMATHGoogle Scholar
  2. 2.
    Garulli, A., Reinelt, W.: Model error modeling in set membership identification. In: Proc. of the System Identification Symposium (2000)Google Scholar
  3. 3.
    Goodwin, G., Braslavsky, J., Seron, M.: Non-stationary stochastic embedding for transfer function estimation. In: Proc. of the 14th IFAC World Congress (1999)Google Scholar
  4. 4.
    Keesman, K.J.: Membership-set estimation using random scanning and principal component analysis. Mathematics and Computers in Simulation 32, 535–544 (1990)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining convergence and diversity in evolutionary multi-objective optimization. Evolutionary computation 10(3) (2002)Google Scholar
  6. 6.
    Milanese, M., Vicino, A.: Optimal Estimation theory for Dynamic Systems with Set Membership Uncertainty: An Overview. Automatica 27(6), 997–1009 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Norton, J., Veres, S.: Identification of nonlinear state-space models by deterministic search. In: Proc. of the IFAC Symposium on Identification and system parameter estimation, vol. 1, pp. 363–368 (1991)Google Scholar
  8. 8.
    Reinelt, W., Garulli, A., Ljung, L.: Comparing different approaches to model error modelling in robust identification. Automatica 38(5), 787–803 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Walter, E., Kieffer, M.: Interval analysis for guaranteed nonlinear parameter estimation. In: Proc. of the 13th IFAC Symposium on System Identification (2003)Google Scholar
  10. 10.
    Walter, E., Piet-Lahanier, H.: Estimation of parameter bounds from bounded-error data: A survey. Mathematics and computers in Simulation 32, 449–468 (1990)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Predictive Control and Heuristic Optimization Group, Department of Systems Engineering and ControlPolytechnic University of Valencia 

Personalised recommendations