Dynamics Identification in Evolution Models Using Radial Basis Functions

The problem of identifying an unknown function of the state of an evolution model with differential equations is considered in the framework of a minimization problem. The well-posedness of this minimization problem as well as unique solvability is proven. The analysis of the dependence of the ident...

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Bibliographic Details
Published in:Journal of dynamical and control systems Vol. 23; no. 2; pp. 317 - 335
Main Authors: Merger, Juri, Borzì, Alfio
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2017
Springer Nature B.V
Subjects:
Calculus of Variations and Optimal Control; Optimization
Control
Differential equations
Dynamical Systems
Dynamical Systems and Ergodic Theory
Evolution
Function space
Mathematics
Mathematics and Statistics
Optimization
Radial basis function
Systems Theory
Vibration
Function identification
Radial basis functions
Infinite dimensional optimization
ISSN:1079-2724, 1573-8698
Online Access:Get full text
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Summary:The problem of identifying an unknown function of the state of an evolution model with differential equations is considered in the framework of a minimization problem. The well-posedness of this minimization problem as well as unique solvability is proven. The analysis of the dependence of the identified function on the data is presented by means of the derivative of the “data–to–function” mapping. Moreover, the infinite dimensional function space, where the unknown function is sought, is discretized by suitable radial basis functions that are chosen such that optimal approximation results are obtained. The numerical treatment of a representative evolution model and the application to a bio-chemical model illustrate the proposed approach.
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ISSN:1079-2724
1573-8698
DOI:10.1007/s10883-016-9322-y