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Minimizing Sequences for a Family of Functional Optimal Estimation Problems

Author

Listed:
  • Angelo Alessandri

    (University of Genoa)

  • Giorgio Gnecco

    (University of Genoa)

  • Marcello Sanguineti

    (University of Genoa)

Abstract

Rates of convergence are derived for approximate solutions to optimization problems associated with the design of state estimators for nonlinear dynamic systems. Such problems consist in minimizing the functional given by the worst-case ratio between the ℒ p -norm of the estimation error and the sum of the ℒ p -norms of the disturbances acting on the dynamic system. The state estimator depends on an innovation function, which is searched for as a minimizer of the functional over a subset of a suitably-defined functional space. In general, no closed-form solutions are available for these optimization problems. Following the approach proposed in (Optim. Theory Appl. 134:445–466, 2007), suboptimal solutions are searched for over linear combinations of basis functions containing some parameters to be optimized. The accuracies of such suboptimal solutions are estimated in terms of the number of basis functions. The estimates hold for families of approximators used in applications, such as splines of suitable orders.

Suggested Citation

  • Angelo Alessandri & Giorgio Gnecco & Marcello Sanguineti, 2010. "Minimizing Sequences for a Family of Functional Optimal Estimation Problems," Journal of Optimization Theory and Applications, Springer, vol. 147(2), pages 243-262, November.
    • Handle: RePEc:spr:joptap:v:147:y:2010:i:2:d:10.1007_s10957-010-9720-3
    DOI: 10.1007/s10957-010-9720-3
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    References listed on IDEAS

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    1. R. Zoppoli & M. Sanguineti & T. Parisini, 2002. "Approximating Networks and Extended Ritz Method for the Solution of Functional Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 403-440, February.
    2. A. Alessandri & C. Cervellera & M. Sanguineti, 2007. "Functional Optimal Estimation Problems and Their Solution by Nonlinear Approximation Schemes," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 445-466, September.
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    Citations

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    Cited by:

    1. Mauro Gaggero & Giorgio Gnecco & Marcello Sanguineti, 2013. "Dynamic Programming and Value-Function Approximation in Sequential Decision Problems: Error Analysis and Numerical Results," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 380-416, February.

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