Relations between frequency‐dependent control and state weighting in LQG problems

B. D.O. Anderson; J. B. Moore; D. L. Mingori

doi:10.1002/oca.4660080202

Relations between frequency‐dependent control and state weighting in LQG problems

B. D.O. Anderson^*, J. B. Moore, D. L. Mingori

^*Corresponding author for this work

The Australian National University

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

This paper considers the relation between controller designs for the same linear system achieved with two different quadratic performance indices. These indices differ only to the extent that one has frequency weighting on the control whereas the other has the inverse frequency weighting on the state. The feedback controllers are constructed by augmenting the given plant and by solving a modified LQG problem for the augmented system. The main result is that whereas the optimal controls as time functions can be the same, the optimal controllers are different. Filtering results are also obtained.

Original language	English
Pages (from-to)	109-127
Number of pages	19
Journal	Optimal Control Applications and Methods
Volume	8
Issue number	2
DOIs	https://doi.org/10.1002/oca.4660080202
Publication status	Published - 1987

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title = "Relations between frequency‐dependent control and state weighting in LQG problems",

abstract = "This paper considers the relation between controller designs for the same linear system achieved with two different quadratic performance indices. These indices differ only to the extent that one has frequency weighting on the control whereas the other has the inverse frequency weighting on the state. The feedback controllers are constructed by augmenting the given plant and by solving a modified LQG problem for the augmented system. The main result is that whereas the optimal controls as time functions can be the same, the optimal controllers are different. Filtering results are also obtained.",

keywords = "Frequency‐shaped cost functionals, Linear‐quadratic controller design, Optimal filtering, Robust design, State and control frequency weighting",

author = "Anderson, {B. D.O.} and Moore, {J. B.} and Mingori, {D. L.}",

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AB - This paper considers the relation between controller designs for the same linear system achieved with two different quadratic performance indices. These indices differ only to the extent that one has frequency weighting on the control whereas the other has the inverse frequency weighting on the state. The feedback controllers are constructed by augmenting the given plant and by solving a modified LQG problem for the augmented system. The main result is that whereas the optimal controls as time functions can be the same, the optimal controllers are different. Filtering results are also obtained.

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KW - Optimal filtering

KW - Robust design

KW - State and control frequency weighting

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Relations between frequency‐dependent control and state weighting in LQG problems

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