On Stability of Guaranteed Estimation Problems: Error Bounds for Information Domains and Experimental Design

  • Mikhail I. Gusev
  • Sergei A. Romanov
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 57)


The two guaranteed estimation problems related to semi-infinite programming theory are considered. For abstract estimation problem in a Banach space we study the dependence of information domains ([12], [14]) on measurement errors with intensity of errors tending to zero. The upper estimates for the rate of convergence of information domains to their limit in the Hausdorff metric are given. The experimental design problem for estimation of distributed system with uncertain parameters through available measurements is also considered in the context of guaranteed estimation theory. For the stationary sensor placement problem we describe its reduction to a nonlinear programming problem. In the case of sufficiently large number of sensors it is shown that the solution may be obtained by solving linear semi-infinite programming problem.


Optimal Control Problem Uncertain Parameter Uncertain System Linear Continuous Operator Sensor Placement 
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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Mikhail I. Gusev
    • 1
  • Sergei A. Romanov
    • 1
  1. 1.Institute of Mathematics and MechanicsUral Branch of the Russian Academy of SciencesEkaterinburgRussia

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