### On the Choice of Sampling Rates in Optimal Linear Systems

(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)

Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/207dff65-0b02-4e9f-9cf4-cbc1301492bf

- author
- Åström, Karl Johan
^{LU} - organization
- publishing date
- 1963-04-25
- type
- Book/Report
- publication status
- published
- subject
- in
- IBM Research: Engineering Studies
- pages
- 87 pages
- publisher
- IBM Corporation
- language
- English
- LU publication?
- yes
- id
- 207dff65-0b02-4e9f-9cf4-cbc1301492bf
- date added to LUP
- 2017-02-27 10:07:09
- date last changed
- 2020-07-06 15:39:40

@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 Corporation}}, language = {{eng}}, month = {{04}}, series = {{IBM Research: Engineering Studies}}, title = {{On the Choice of Sampling Rates in Optimal Linear Systems}}, url = {{https://lup.lub.lu.se/search/files/21969369/ast63IBM.pdf}}, year = {{1963}}, }