A convex relaxation approach to set-membership identification
type: CreativeWork
description: Set-membership identification of dynamical systems is dealt with in this thesis. Differently from the stochastic framework, in the set-membership context the statistical description of the measurement noise is not available and the only information on such an error is that its amplitude or energy is bounded. In the framework of Set-membership identification, the result of the estimation process is the set of all system parameter values consistent with measured data, assumed model structure and a-priori assumptions on the measurement error. The problem of evaluating bounds on system parameters belonging to the feasible parameter set can be formulated in terms of polynomial optimization problems, where the number of decision variables increases with the length of the experimental data sequence. Such problems are generally nonconvex and NP-hard. Therefore, standard nonlinear optimization tools can not be used to compute parameter bounds, since they can trap in local minima and, as a consequence, the computed bounds are not guaranteed to contain the true values of parameters, which is a key requirement in set-membership identification. In order to overcome such a problem, convex relaxation procedures based on the theory of moments are proposed to efficiently compute relaxed bounds which are guaranteed to contain the true values of system parameters. Unfortunately, a direct application of the theory of moments in relaxing set-membership identification problems leads to semidefinite programming problems with high computational burden, thus limiting, in practice, the use of such relaxation procedures to solve identification problems with a small number of measurements. The aim of the thesis is to derive a number of convex-relaxation based algorithms that, exploiting the peculiar properties of the considered identification problems, make it possible to perform bound computation also when the number of measurements is large. In particular, errors-in-variables (EIV) identific…
abstract: Set-membership identification of dynamical systems is dealt with in this thesis. Differently from the stochastic framework, in the set-membership context the statistical description of the measurement noise is not available and the only information on such an error is that its amplitude or energy is bounded. In the framework of Set-membership identification, the result of the estimation process is the set of all system parameter values consistent with measured data, assumed model structure and a-priori assumptions on the measurement error. The problem of evaluating bounds on system parameters belonging to the feasible parameter set can be formulated in terms of polynomial optimization problems, where the number of decision variables increases with the length of the experimental data sequence. Such problems are generally nonconvex and NP-hard. Therefore, standard nonlinear optimization tools can not be used to compute parameter bounds, since they can trap in local minima and, as a consequence, the computed bounds are not guaranteed to contain the true values of parameters, which is a key requirement in set-membership identification. In order to overcome such a problem, convex relaxation procedures based on the theory of moments are proposed to efficiently compute relaxed bounds which are guaranteed to contain the true values of system parameters. Unfortunately, a direct application of the theory of moments in relaxing set-membership identification problems leads to semidefinite programming problems with high computational burden, thus limiting, in practice, the use of such relaxation procedures to solve identification problems with a small number of measurements. The aim of the thesis is to derive a number of convex-relaxation based algorithms that, exploiting the peculiar properties of the considered identification problems, make it possible to perform bound computation also when the number of measurements is large. In particular, errors-in-variables (EIV) identific…
author: PIGA, DARIO
language: eng
keywords: Settore ING-INF/04 - Automatica
date published: 2012
date modified: 2026-07-24T03:51:05Z
provider: Politecnico di Torino
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Politecnico di Torino

PropertyValue
property ID: Handle
value: http://hdl.handle.net/11583/2497251