Guaranteed estimation of the parameters of nonlinear continuous-time models: contributions of interval analysis
Résumé
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.
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