eprintid: 1716
rev_number: 7
eprint_status: archive
userid: 46
dir: disk0/00/00/17/16
datestamp: 2013-09-13 10:33:43
lastmod: 2013-09-16 12:03:00
status_changed: 2013-09-13 10:33:43
type: article
metadata_visibility: show
creators_name: Alessandri, Angelo
creators_name: Gnecco, Giorgio
creators_name: Sanguineti, Marcello
creators_id: 
creators_id: giorgio.gnecco@imtlucca.it
creators_id: 
title: Minimizing Sequences for a Family of Functional Optimal Estimation Problems
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: none
keywords: Infinite-dimensional optimization; Optimal estimation; Minimizing sequences; Approximation rates
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.
date: 2010
date_type: published
publication: Journal of Optimization Theory and Applications
volume: 147
number: 2
publisher: Springer-Verlag
pagerange: 243-262
id_number: 10.1007/s10957-010-9720-3
refereed: TRUE
issn: 0022-3239
official_url: http://dx.doi.org/10.1007/s10957-010-9720-3
projects: Partially supported by the project Ateneo 2008 “Solution of functional optimization problems by nonlinear approximators and learning from data” of the University of Genoa
citation:   Alessandri, Angelo and Gnecco, Giorgio and Sanguineti, Marcello  Minimizing Sequences for a Family of Functional Optimal Estimation Problems.  Journal of Optimization Theory and Applications, 147 (2).  pp. 243-262.  ISSN 0022-3239      (2010)