Adaptive Algorithms in Finite Forms

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dc.creatorTyukin, I. Y.
dc.creatorProkhorov, D. V.
dc.creatorvan Leeuwen, Cees
dc.date2003-09-16
dc.date2003-11-05
dc.date.accessioned2026-07-07T05:01:09Z
dc.date.available2026-07-07T05:01:09Z
dc.descriptionWe propose a new method to design adaptation algorithms that guarantee a certain prescribed level of performance and are applicable to systems with nonconvex parameterization. The main idea behind the method is, given the desired performance characteristics and a class of nonlinearly parameterized systems, first to augment the tuning error function and design the adaptation scheme in the form of ordinary differential equations. The resulting augmentation is allowed to depend on state derivatives. To deal with these, we suggest the realization of the adaptation scheme in an algebraic-integral form. Because of the explicit dependance on the state of the original system such adaptation schemes are referred to as adaptive algorithms in it finite form instead of differential ones. Sufficient conditions for the existence of finite form realizations are proposed. These conditions lead to the necessity to find a solution of a system of partial differential equations, which in general is not an easy task. In order to resolve this problem we suggest to embed the original system dynamics into one of a higher order, thus replacing it by a simple integration of a function with respect to a single scalar argument. Several full-state feedback finite form realizations are presented and illustrated with examples.
dc.description32 pages, 1 figure, preliminary version was published in Proceedings of European Control Conference 2003, Cambridge, UK
dc.identifierhttps://arxiv.org/abs/math/0309254
dc.identifierhttp://arxiv.org/abs/math/0309254
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68573
dc.subjectOptimization and Control
dc.subjectDynamical Systems
dc.titleAdaptive Algorithms in Finite Forms
dc.typetext

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