Advertisement

Recent results on the analytic center approach for bounded error parameter estimation

  • Er-Wei Bai
  • Roberto Tempo
  • Yinyu Ye
Part C Modeling, Identification And Estimation
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 241)

Abstract

In this paper, we present an overview of some recent work [5] on the so-called analytic center approach for bounded error parameter estimation. First, we discuss the optimality properties of well-known algorithms such as the Chebychev center, the projection and the min-max estimates. Subsequently, we propose the analytic center as an alternative algorithm for recursive estimation. We show that the analytic center minimizes the output error and, on the contrary of other estimates like Chebychev, allows for an easy-to-compute sequential algorithm. We argue that the maximum number of Newton iterations required to evaluate a sequence of analytic centers is linear in the number of observed data points and it is comparable to the complexity of off-line algorithms for estimating a single analytic center. Finally, we briefly discuss a number of open problems which are currently under investigation.

Keywords

Linear Matrix Inequality Analytic Center Interior Point Method Newton Iteration Output Error 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    (1995). “Special Issue on Bounded Error Estimation (Part II),” International Journal of Adaptive Control and Signal Processing, Vol. 9.Google Scholar
  2. [2]
    (1992). “Special Issue on System Identification for Robust Control Design,” IEEE Transactions on Automatic Control, Vol. 37.Google Scholar
  3. [3]
    (1995). “Special Issue on Trends in System Identification,” Automatica, Vol. 31.Google Scholar
  4. [4]
    Afkhamie, K. H., Z.-Q. Luo and K. M. Wong (1997). “Interior Point Column Generation Algorithms for Adaptive Fltering,” Technical Report Mc Master University, Ontario, Canada.Google Scholar
  5. [5]
    Bai, E.-W., Y. Ye and R. Tempo (1997). “Bounded Error Parameter Estimation: A Sequential Analytic Center Approach,’ Proceedings of the IEEE Conference on Decision and Control, San Diego; also submitted to IEEE Transactions on Automatic Control.Google Scholar
  6. [6]
    Bai, E.-W., M. Fu, R. Tempo and Y. Ye (1997). “Analytic Center Approach to Parameter Estimation: Convergence Analysis,” Technical Report University of Newcastle, Newcastle, Australia.Google Scholar
  7. [7]
    Bai, E.-W., R. Tempo and Y. Ye (1997). “Open Problems in Sequential Parametric Estimation,” Technical Report CENS-CNR, Politecnico di Torino, Torino, Italy.Google Scholar
  8. [8]
    Boyd, S., L. El Ghaoui, E. Feron and V. Balakrishnan (1994). Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA.zbMATHGoogle Scholar
  9. [9]
    Fogel, E. and Y. Huang (1982). “On the value of information in system identification-bounded noise case,” Automatica, Vol. 18, pp. 229–238.zbMATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    Goffin, J. L., Z. Luo, and Y. Ye (1996). “Complexity analysis of an interior cutting plane method for convex feasibility problems,” SIAM J. Optimization, Vol. 6, pp. 638–652.zbMATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    Ljung, L. (1995). “System Identification: Theory for the Users,” Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
  12. [12]
    Milanese M. and R. Tempo, “Optimal Algorithms Theory for Robust Estimation and Prediction,” IEEE Transactions on Automatic Control, vol. AC-30, pp. 730–738, 1985.CrossRefMathSciNetGoogle Scholar
  13. [13]
    Ninness, B. M. and G. C. Goodwin (1995). “Rapproachement between bounded-error and stochastic estimation theory”, International Journal Adaptive Control and Signal Processing, Vol. 9, pp. 107–132.zbMATHCrossRefMathSciNetGoogle Scholar
  14. [14]
    Sonnevend, G. (1986). “An analytic center for polyhedrons and new classes of global algorithms for linear programming,” Lecture Notes in Control and Information Science, Vol. 84, pp. 866–876.MathSciNetGoogle Scholar
  15. [15]
    Sonnevend, G. (1987). “A new method for solving a set of linear inequalities and its applications,” Dynamic Modelling and Control of National Economics, Pergamon, Oxford-New York, pp. 465–471.Google Scholar
  16. [16]
    Traub, J. F., G. Wasikowski and H. Wozniakowski (1988). Information-Based Complexity, Academic, New York.zbMATHGoogle Scholar
  17. [17]
    Ye, Y. (1997). Interior-Point Algorithm: Theory and Analysis, Wiley, New York.Google Scholar

Copyright information

© Springer-Verlag London Limited 1999

Authors and Affiliations

  • Er-Wei Bai
    • 1
  • Roberto Tempo
    • 2
  • Yinyu Ye
    • 3
  1. 1.Department of Electrical and Computer EngineeringUniversity of IowaIowa City
  2. 2.CENS-CNR, Politecnico di TorinoTorinoItaly
  3. 3.Department of Management ScienceUniversity of IowaIowa City

Personalised recommendations