NDLI: Sub-Optimal Control in Presence of Unobservable Disturbances

Content Provider	IEEE Xplore Digital Library
Author	Quincampoix, M. Veliov, V.M.
Copyright Year	2005
Description	Author affiliation: Laboratoire de Mathématiques, Unité CNRS UMR 6205, Université de Bretagne Occidentale, 6 Avenue Victor Le Gorgeu, 29200 Brest, France, Marc.Quincampoix@univ-brest.fr (Quincampoix, M.)
Abstract	We investigate the problem of optimization of a terminal cost function for a system depending on a control, and on two disturbances for which a priori set membership is known. The disturbances are of different natures: One becomes known to the controller at the current time (we called it observable) while the other remains unknown. The state of the system is not measured, therefore not exactly known due to the presence of an unobservable disturbance. We reformulate the problem through a set-valued dynamics describing the evolution of the current set estimation of the state. To reduce the complexity of the problem, we pass to a suboptimal problem where the evolution of the state estimation is restricted to a prescribed collection of sets. The main result of the paper is a characterization of the value function of this problem through a Hamilton–Jacobi inequality in terms of Dini derivatives, which implies a convergent scheme for numerical computations. As necessary auxiliary tools, we provide new results on evolution and viability of tubes in a given collection of sets.
Starting Page	5877
Ending Page	5882
File Size	169895
Page Count	6
File Format	PDF
ISBN	0780395670
DOI	10.1109/CDC.2005.1583101
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2005-12-15
Publisher Place	Spain
Access Restriction	Subscribed
Rights Holder	IEEE/EUCA
Subject Keyword	Uncertainty Control systems State estimation Open loop systems Cost function Feedback Mathematics Informatics Dynamic programming Optimal control
Content Type	Text
Resource Type	Article

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