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On the Choice of Sampling Rates in Optimal Linear Systems

Åström, Karl Johan LU (1963) In IBM Research: Engineering Studies
Abstract
In a sample data system we are essentially restricted to control signals which are constant over the sampling interval. The purpose of this report is to analyze the effect of this restriction. The situation where the admissible control signals are piecewise continuous is used as a reference case and the problem is approached from a variational formulation of the control problem where the object of the control is to minimize a loss function.
The minimal values of the loss function over the classes of piecewise constant and piecewise continuous control signals are compared. It is assumed that the system is linear and the criterion quadratic. Asymptotic formulas for small sampling intervals and Fortran programs for the evaluation of the... (More)
In a sample data system we are essentially restricted to control signals which are constant over the sampling interval. The purpose of this report is to analyze the effect of this restriction. The situation where the admissible control signals are piecewise continuous is used as a reference case and the problem is approached from a variational formulation of the control problem where the object of the control is to minimize a loss function.
The minimal values of the loss function over the classes of piecewise constant and piecewise continuous control signals are compared. It is assumed that the system is linear and the criterion quadratic. Asymptotic formulas for small sampling intervals and Fortran programs for the evaluation of the values of the loss function in the discrete and continuous cases are given. (Less)
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author
organization
publishing date
type
Book/Report
publication status
published
subject
in
IBM Research: Engineering Studies
pages
87 pages
publisher
IBM Corp
language
English
LU publication?
yes
id
207dff65-0b02-4e9f-9cf4-cbc1301492bf
date added to LUP
2017-02-27 10:07:09
date last changed
2017-02-27 10:07:09
@techreport{207dff65-0b02-4e9f-9cf4-cbc1301492bf,
  abstract     = { In a sample data system we are essentially restricted to control signals which are constant over the sampling interval. The purpose of this report is to analyze the effect of this restriction. The situation where the admissible control signals are piecewise continuous is used as a reference case and the problem is approached from a variational formulation of the control problem where the object of the control is to minimize a loss function.<br/>The minimal values of the loss function over the classes of piecewise constant and piecewise continuous control signals are compared. It is assumed that the system is linear and the criterion quadratic. Asymptotic formulas for small sampling intervals and Fortran programs for the evaluation of the values of the loss function in the discrete and continuous cases are given.},
  author       = {Åström, Karl Johan},
  institution  = {IBM Corp},
  language     = {eng},
  month        = {04},
  pages        = {87},
  series       = {IBM Research: Engineering Studies},
  title        = {On the Choice of Sampling Rates in Optimal Linear Systems},
  year         = {1963},
}