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Optimal Estimation Theory for Dynamic Systems with Set Membership Uncertainty: An Overview

  • M. Milanese
  • A. Vicino

Abstract

In many problems, such as linear and nonlinear regressions, parameter and state estimation of dynamic systems, state space and time series prediction, interpolation, smoothing, and functions approximation, one has to evaluate some unknown variable using available data. The data are always associated with some uncertainty and it is necessary to evaluate how this uncertainty affects the estimated variables. Typically, the problem is approached assuming a probabilistic description of uncertainty and applying statistical estimation theory. An interesting alternative, referred to as set membership or unknown but bounded (UBB) error description, has been investigated since the late 60s. In this approach, uncertainty is described by an additive noise which is known only to have given integral (typically l 1 or l 2) or componentwise (l ) bounds. In this chapter the main results of this theory are reviewed, with special attention to the most recent advances obtained in the case of componentwise bounds.

Keywords

Linear Programming Problem Recursive Algorithm Information Operator Correct Estimator Problem Element 
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.

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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • M. Milanese
    • 1
  • A. Vicino
    • 2
  1. 1.Dipartimento di Automatica e InformaticaPolitecnico di TorinoTorinoItaly
  2. 2.Facoltà di IngegneriaUniversità degli Studi di SienaSienaItaly

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