Methods of constructing optimal stabilizers
type: Item
instance of: scholarly article
title: Methods of constructing optimal stabilizers
zbMATH Open document ID: 0810.49002
DOI: 10.1016/0021-8928(93)90076-X
published in: Journal of Applied Mathematics and Mechanics
publication date: 1994-12-06T00:00:00Z
review text: The problem of transforming a linear dynamical system of the form \(\dot x= Ax\) in the neighbourhood of a state equilibrium is solved using the special problem of the damping of the system \[ \dot x= Ax+ bu,\quad t\geq 0,\quad x(0)= x_ 0, \] by controls of minimum intensity after a finite time interval. The system is called dampened if the property \(| x_ i(\theta)|\leq \varepsilon\), \(i\in I= \{1,2,\dots,n\}\) is satisfied for each initial state \(x_ 0\) (\((0,\theta)\) is the finite time interval of programmed damping). The proposed method is based on the constructive theory of optimal control. An example is given.
Mathematics Subject Classification ID: 49J15
zbMATH DE Number: 699555
zbMATH Keywords: linear dynamical system
zbMATH Keywords: state equilibrium
zbMATH Keywords: damping
zbMATH Keywords: initial state
zbMATH Keywords: optimal control
author: Rafail Gabasov
author: Faina Mihaǐlovna Kirillova
reviewed by: Hans Benker
MaRDI profile type: Publication
cites work: Q5509213
cites work: Q4326168
cites work: The theory of analytic design of controllers
cites work: Q3703580
cites work: Q4695927
cites work: Q4033354
full work available at URL: 0021-8928(93)90076-x
OpenAlex ID: W2092277812
description: scientific article; zbMATH DE number 699555