Linear Controllers are Uniformly Optimal for the Witsenhausen Counterexample

In 1968, Witsenhausen introduced his celebrated counterexample, which illustrated that when an information pattern is nonclassical, the controllers which optimize an expected quadratic cost may be nonlinear. It is shown here that for the Witsenhausen counterexample, when one instead considers the in...

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Bibliographic Details
Published inProceedings of the 45th IEEE Conference on Decision and Control pp. 553 - 558
Main Author Rotkowitz, M.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.12.2006
SeriesProceedings of the IEEE Conference on Decision and Control
Subjects
Centralized control
Control systems
Cost function
Gaussian noise
Information patterns
Linear control systems
Noise figure
Nonclassical
Nonlinear control systems
Optimal control
Optimal control systems
Optimization
Quadratic costs
Quadratic programming
USA Councils
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ISBN9781424401710
1424401712
ISSN0191-2216
DOI10.1109/CDC.2006.377259

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Summary:In 1968, Witsenhausen introduced his celebrated counterexample, which illustrated that when an information pattern is nonclassical, the controllers which optimize an expected quadratic cost may be nonlinear. It is shown here that for the Witsenhausen counterexample, when one instead considers the induced norm, then linear controllers are in fact optimal
ISBN:9781424401710
1424401712
ISSN:0191-2216
DOI:10.1109/CDC.2006.377259