A Counterexample in Stochastic Optimum Control

It is sometimes conjectured that nothing is to be gained by using non-linear controllers when the objective is to minimize the expectation of a quadratic criterion for a linear system subject to Gaussian noise and with unconstrained control variables. In fact, this statement has only been establishe...

Full description

Saved in:
Bibliographic Details
Published inSIAM journal on control Vol. 6; no. 1; pp. 131 - 147
Main Author Witsenhausen, H. S.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.02.1968
Subjects
Decision theory
Expected values
Laplace transforms
Noise
Random variables
Online AccessGet full text
ISSN0036-1402
0363-0129
1095-7138
DOI10.1137/0306011

Cover

More Information
Summary:It is sometimes conjectured that nothing is to be gained by using non-linear controllers when the objective is to minimize the expectation of a quadratic criterion for a linear system subject to Gaussian noise and with unconstrained control variables. In fact, this statement has only been established for the case where all control variables are generated by a single station which has perfect memory. Without this qualification the conjecture is false.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0036-1402
0363-0129
1095-7138
DOI:10.1137/0306011