A Newton-Raphson algorithm for calculating the effects of changes in weights on an H∞ design

Alexander Lanzon; Brian D.O. Anderson; Xavier Bombois

doi:10.1109/CDC.2005.1582730

A Newton-Raphson algorithm for calculating the effects of changes in weights on an H_∞ design

Alexander Lanzon^*, Brian D.O. Anderson, Xavier Bombois

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

When weights are adjusted in an H_∞ design, corresponding modifications occur in the synthesised H_∞ controller and the resulting closed-loop transfer function matrices of interest. This article proposes an algorithm that allow us to compute the corresponding modifications hi the controller and closed-loop transfer functions via calculations that are simpler/faster than solving two brand new Riccati equations from scratch. This is particularly beneficial (in terms of both speed and numerical reliability of the solutions) for high order systems and in iterative adaptive control algorithms that involve weight adjustments at each sampling interval. The algorithm proposed here builds upon our previous results presented in [1] and now allow us to also handle medium-size and large weight adjustments, as opposed to only small weight adjustments.

Original language	English
Title of host publication	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Pages	3657-3662
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2005.1582730
Publication status	Published - 2005
Event	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain Duration: 12 Dec 2005 → 15 Dec 2005

Publication series

Name	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Volume	2005

Conference

Conference	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Country/Territory	Spain
City	Seville
Period	12/12/05 → 15/12/05

Access to Document

10.1109/CDC.2005.1582730

Cite this

Lanzon, A., Anderson, B. D. O., & Bombois, X. (2005). A Newton-Raphson algorithm for calculating the effects of changes in weights on an H_∞ design. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 (pp. 3657-3662). Article 1582730 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005). https://doi.org/10.1109/CDC.2005.1582730

Lanzon, Alexander ; Anderson, Brian D.O. ; Bombois, Xavier. / A Newton-Raphson algorithm for calculating the effects of changes in weights on an H_∞ design. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. pp. 3657-3662 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05).

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abstract = "When weights are adjusted in an H∞ design, corresponding modifications occur in the synthesised H∞ controller and the resulting closed-loop transfer function matrices of interest. This article proposes an algorithm that allow us to compute the corresponding modifications hi the controller and closed-loop transfer functions via calculations that are simpler/faster than solving two brand new Riccati equations from scratch. This is particularly beneficial (in terms of both speed and numerical reliability of the solutions) for high order systems and in iterative adaptive control algorithms that involve weight adjustments at each sampling interval. The algorithm proposed here builds upon our previous results presented in [1] and now allow us to also handle medium-size and large weight adjustments, as opposed to only small weight adjustments.",

keywords = "Chain-scattering, H-control, J-lossless factorisation, Weight adjustments, Weight modifications",

author = "Alexander Lanzon and Anderson, {Brian D.O.} and Xavier Bombois",

year = "2005",

doi = "10.1109/CDC.2005.1582730",

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series = "Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05",

pages = "3657--3662",

booktitle = "Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05",

note = "44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 ; Conference date: 12-12-2005 Through 15-12-2005",

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Lanzon, A, Anderson, BDO & Bombois, X 2005, A Newton-Raphson algorithm for calculating the effects of changes in weights on an H_∞ design. in Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05., 1582730, Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, vol. 2005, pp. 3657-3662, 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, Seville, Spain, 12/12/05. https://doi.org/10.1109/CDC.2005.1582730

A Newton-Raphson algorithm for calculating the effects of changes in weights on an H_∞ design. / Lanzon, Alexander; Anderson, Brian D.O.; Bombois, Xavier.
Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 3657-3662 1582730 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Lanzon A, Anderson BDO, Bombois X. A Newton-Raphson algorithm for calculating the effects of changes in weights on an H_∞ design. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 3657-3662. 1582730. (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05). doi: 10.1109/CDC.2005.1582730