Cheap control problem of a linear uniform rank system: Design by composite control
type: Item
instance of: scholarly article
title: Cheap control problem of a linear uniform rank system: Design by composite control
zbMATH Open document ID: 0602.93031
DOI: 10.1016/0005-1098(86)90017-8
published in: Automatica
publication date: 1986-01-01T00:00:00Z
review text: Cheap control problems where a small parameter \(\mu^ 2\) multiplies the control cost are considered. Due to the cheapness of control, a strong control action in the form of high-gain feedback forces the given system to have slow and fast, low and high amplitude variations. For a class of linear systems (uniform rank systems), a systematic procedure of amplitude scaling and time-scale decomposition which normalizes high and low amplitude variations and which separates slow anf fast time scales is presented. The method permits the explicit characterization of all the limiting properties of the considered cheap control problem as \(\mu\to 0\). Methods of calculating singular controls and how non-uniqueness can arise in them are discussed. Above all, several suboptimal composite control schemes are developed based on the decomposition of the given optimal design into two lower order subsystem designs.
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 93C35
Mathematics Subject Classification ID: 93D20
zbMATH DE Number: 3972738
zbMATH Keywords: Cheap control
zbMATH Keywords: time-scale decomposition
zbMATH Keywords: singular controls
zbMATH Keywords: suboptimal composite control schemes
author: Ali Saberi
author: Peddapullaiah Sannuti
MaRDI profile type: Publication
full work available at URL: 0005-1098(86)90017-8
OpenAlex ID: W2064407247
cites work: A decomposition of near-optimum regulators for systems with slow and fast modes
cites work: The optimal linear-quadratic time-invariant regulator with cheap control
cites work: On a class of optimal control problems with an almost cost-free solution
cites work: Quadratic weights for asymptotic regulator properties
cites work: Singular perturbations and order reduction in control theory - an overview
cites work: Asymptotic root loci of multivariable linear optimal regulators
cites work: Singular perturbations and singular arcs--Part II
cites work: Direct singular perturbation analysis of high-gain and cheap control problems
cites work: Multiple time-scale decomposition in cheap control problems--Singular control
cites work: The optimal LQ regulator with cheap control for not strictly proper systems
cites work: A singular perturbation analysis of high-gain feedback systems
description: scientific article; zbMATH DE number 3972738