How violent are fast controls? II
type: Item
instance of: scholarly article
title: How violent are fast controls? II
zbMATH Open document ID: 0906.93007
DOI: 10.1007/BF01211854
author: Thomas I. Seidman
author: Jiongmin Yong
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 1998-10-06T00:00:00Z
review text: [For Part I by the first author see ibid. 1, No. 1, 89-95 (1988; Zbl 0663.49018).] The authors consider a linear time-dependent control system \[ \dot x=Ax+Bu \] and the problem of minimizing the \(L^p\)-norm \(\| u\|_p\) subject to \[ x(0)=0, \qquad x(T)=\xi \] when \(T\rightarrow 0\). The main result is that the asymptotic part of the minimizing norm is \[ (1/T)^{k+1-1/p},\quad p\in [1,+\infty] \] where \(k=\min\{j: \xi\in \text{range} (B+AB+\cdots +A^jB\}\). Finally a representation formula is given for the minimizing control.
reviewed by: Gianna Stefani
Mathematics Subject Classification ID: 93B03
Mathematics Subject Classification ID: 49N05
Mathematics Subject Classification ID: 93C05
zbMATH DE Number: 1018714
zbMATH Keywords: linear systems
zbMATH Keywords: minimum-norm control
zbMATH Keywords: asymptotics
MaRDI profile type: Publication
cites work: Q3996569
cites work: How violent are fast controls?
cites work: Q3751436
cites work: Q3874718
full work available at URL: https://doi.org/10.1007/bf01211854
OpenAlex ID: W4230342170
description: scientific article; zbMATH DE number 1018714