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Guaranteed estimation of the parameters of nonlinear continuous‐time models: Contributions of interval analysis
Author(s) -
Kieffer M.,
Walter E.
Publication year - 2011
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.1194
Subject(s) - bounded function , context (archaeology) , interval (graph theory) , estimation theory , set (abstract data type) , estimation , sensitivity (control systems) , nonlinear system , mathematical optimization , computer science , function (biology) , interval estimation , interval arithmetic , mathematics , control theory (sociology) , algorithm , statistics , artificial intelligence , confidence interval , engineering , control (management) , systems engineering , electronic engineering , mathematical analysis , biology , paleontology , quantum mechanics , evolutionary biology , programming language , physics , combinatorics
This paper is about guaranteed parameter estimation in two contexts, namely bounded‐error and optimal estimation. In bounded‐error estimation, one looks for the set of all parameter vectors that are consistent with some prior bounds on the errors deemed acceptable between the model behavior and that of the system. In optimal estimation, one looks for the set of all parameter vectors that minimize some cost function quantifying the discrepancy between the behaviors of the system and its model. In both cases, guaranteed means that proven statements are made about the set of interest. The situation is made much more difficult when the model output is assumed to depend nonlinearly in the parameters to be estimated and when dealing with continuous‐time models, as here. Important tools based on interval analysis (IA) that contribute to allowing guaranteed estimation in these challenging conditions are presented. Some are absolutely classical in the context of IA but not so well known in the community of parameter estimation at large. Others have been developed recently and were mainly presented in conferences. Some, such as the use of sensitivity functions to reduce more quickly the size of outer approximations of the sets of interest, are new. Challenges for future research in the context of guaranteed nonlinear estimation are mentioned. Copyright © 2010 John Wiley & Sons, Ltd.