Closable feedback for guaranteed optimimization of undeterminate systems of control
type: Item
instance of: scholarly article
title: Closable feedback for guaranteed optimimization of undeterminate systems of control
zbMATH Open document ID: 0916.93028
published in: Doklady Mathematics
publication date: 1999-07-12T00:00:00Z
review text: The paper deals with the construction of an optimal control for a linear uncertain system. The uncertainty is represented by an unknown additive piecewise continuous perturbation parameter. The state is assumed to be available for feedback at any current instant of time \(\tau \). Essentially, the ``best control in the worst case'' is considered, and the current value of the optimal control is used defining in this manner a feedback. The main idea of the proposed method is to refine the optimization procedure by dividing the future time interval into two parts and performing a ``closing'' at the joint time instant. This leads to the notions of ``openable optimal feedback'' and ``optimal regulator''. To reduce the computational complexity, certain approximations are considered so that the proposed control is completely determined by a finite number of parameters. These parameters can be found from the so-called determining equations. To improve the quality of the feedback a generalized version of the method is proposed: the future time interval has to be divided into several parts with multiple ``closing'' at the joint time instants.
Mathematics Subject Classification ID: 93B52
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 49N30
Mathematics Subject Classification ID: 49N35
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93C73
zbMATH DE Number: 1113088
zbMATH Keywords: optimal feedback
zbMATH Keywords: linear systems
zbMATH Keywords: perturbations
zbMATH Keywords: numerical methods
zbMATH Keywords: openable optimal feedback
zbMATH Keywords: optimal regulator
author: Rafail Gabasov
author: Faina Mihaǐlovna Kirillova
author: E. A. Kostina
reviewed by: É. Gyurkovics
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1113088