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Optimal and suboptimal algorithms in set membership identification

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  • Bolesław Kacewicz

Abstract

We discuss in this paper optimality properties of identification algorithms in a set membership framework. We deal with restricted-complexity (conditional) identification, where approximations (models) to a possibly complex system are selected from a low dimensional space. We discuss the worst- and average-case settings. In the worst-case setting, we present results on optimality, or suboptimality, of algorithms based on computing the unconditional or conditional Chebyshev centres of an uncertainty set. In the average-case setting, we show that the optimal algorithm is given by the projection of the unconditional Chebyshev centre. We show explicit formulas for its average errors, allowing us to see the contribution of all problem parameters to the minimal error. We discuss the case of weighted average errors corresponding to non-uniform distributions over uncertainty sets, and show how the weights influence the minimal identification error.

Suggested Citation

  • Bolesław Kacewicz, 2005. "Optimal and suboptimal algorithms in set membership identification," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 11(2), pages 159-169, June.
    • Handle: RePEc:taf:nmcmxx:v:11:y:2005:i:2:p:159-169
    DOI: 10.1080/13873950500068575
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    References listed on IDEAS

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    1. A. Garulli & B. Z. Kacewicz & A. Vicino & G. Zappa, 1999. "Reliability of Projection Algorithms in Conditional Estimation," Journal of Optimization Theory and Applications, Springer, vol. 101(1), pages 1-14, April.
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    1. B. Kacewicz, 2001. "Optimal Conditional Estimation: Average Case Setting," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 649-666, June.

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