Nonlinear H∞ control: Practicality of implementing the cheap sensor case

J. William Helton; Matthew R. James; William M. McEneaney

Nonlinear H^∞ control: Practicality of implementing the cheap sensor case

J. William Helton^*, Matthew R. James, William M. McEneaney

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

1 Citation (Scopus)

Abstract

In [5] we introduced a recipe for nonlinear H^∞ controllers which takes advantage of extra perfect measurements and stated a theorem to the effect that this controller yielded the best possible "H^∞" performance. Pure state feedback is an extreme situation and we treated cases where all but a few states are measured perfectly. In this article we analyze the computational complexity of the online part of the H^∞ controller described in [5]. This has important practical implications. Our conclusion is that in reasonable circumstances (even without using much cleverness) when the number of unknown states is less than or equal to 2 and the total number of states is less than or equal to 12 the online portion of the recipe with a 1 GHz PC to produce about 100 controller updates per second.

Original language	English
Pages (from-to)	2746-2751
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	3
Publication status	Published - 2001
Externally published	Yes
Event	40th IEEE Conference on Decision and Control (CDC) - Orlando, FL, United States Duration: 4 Dec 2001 → 7 Dec 2001

Cite this

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title = "Nonlinear H∞ control: Practicality of implementing the cheap sensor case",

abstract = "In [5] we introduced a recipe for nonlinear H∞ controllers which takes advantage of extra perfect measurements and stated a theorem to the effect that this controller yielded the best possible {"}H∞{"} performance. Pure state feedback is an extreme situation and we treated cases where all but a few states are measured perfectly. In this article we analyze the computational complexity of the online part of the H∞ controller described in [5]. This has important practical implications. Our conclusion is that in reasonable circumstances (even without using much cleverness) when the number of unknown states is less than or equal to 2 and the total number of states is less than or equal to 12 the online portion of the recipe with a 1 GHz PC to produce about 100 controller updates per second.",

keywords = "Information states, Nonlinear H control, Reduced order observers, Reduction of computational complexity",

author = "Helton, {J. William} and James, {Matthew R.} and McEneaney, {William M.}",

year = "2001",

language = "English",

volume = "3",

pages = "2746--2751",

journal = "Proceedings of the IEEE Conference on Decision and Control",

issn = "0743-1546",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

note = "40th IEEE Conference on Decision and Control (CDC) ; Conference date: 04-12-2001 Through 07-12-2001",

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TY - JOUR

T1 - Nonlinear H∞ control

T2 - 40th IEEE Conference on Decision and Control (CDC)

AU - Helton, J. William

AU - James, Matthew R.

AU - McEneaney, William M.

PY - 2001

Y1 - 2001

N2 - In [5] we introduced a recipe for nonlinear H∞ controllers which takes advantage of extra perfect measurements and stated a theorem to the effect that this controller yielded the best possible "H∞" performance. Pure state feedback is an extreme situation and we treated cases where all but a few states are measured perfectly. In this article we analyze the computational complexity of the online part of the H∞ controller described in [5]. This has important practical implications. Our conclusion is that in reasonable circumstances (even without using much cleverness) when the number of unknown states is less than or equal to 2 and the total number of states is less than or equal to 12 the online portion of the recipe with a 1 GHz PC to produce about 100 controller updates per second.

AB - In [5] we introduced a recipe for nonlinear H∞ controllers which takes advantage of extra perfect measurements and stated a theorem to the effect that this controller yielded the best possible "H∞" performance. Pure state feedback is an extreme situation and we treated cases where all but a few states are measured perfectly. In this article we analyze the computational complexity of the online part of the H∞ controller described in [5]. This has important practical implications. Our conclusion is that in reasonable circumstances (even without using much cleverness) when the number of unknown states is less than or equal to 2 and the total number of states is less than or equal to 12 the online portion of the recipe with a 1 GHz PC to produce about 100 controller updates per second.

KW - Information states

KW - Nonlinear H control

KW - Reduced order observers

KW - Reduction of computational complexity

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M3 - Conference article

AN - SCOPUS:0035709270

SN - 0743-1546

VL - 3

SP - 2746

EP - 2751

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

Y2 - 4 December 2001 through 7 December 2001

ER -

Nonlinear H^∞ control: Practicality of implementing the cheap sensor case

Abstract

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