An Iterative Algorithm to Estimate Invariant Sets for Uncertain Systems

Peter Seiler

doi:10.23919/ACC.2018.8431113

An Iterative Algorithm to Estimate Invariant Sets for Uncertain Systems

Peter Seiler

Aerospace Engineering and Mechanics

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

2 Scopus citations

Abstract

This paper develops an iterative algorithm to estimate an invariant set for uncertain systems. The uncertain system is given as a connection of a nominal linear time-invariant system and a perturbation. The input/output behavior of the perturbation is described by integral quadratic constraints (IQCs). The proposed approach incorporates IQCs into a dissipation inequality formulation. One issue is that it is often useful to specify the IQC in the frequency domain or, equivalently, in the time-domain as a 'soft' infinite-horizon constraint. However, the dissipation inequality formulation requires constraints that are valid over all finite time horizons. The main technical result is a finite-horizon bound on soft IQCs constructed using a state-feedback transformation. This forms the basis for the proposed iterative algorithm to estimate invariant sets. A simple example is provided to demonstrate the proposed approach.

Original language	English (US)
Title of host publication	2018 Annual American Control Conference, ACC 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4249-4254
Number of pages	6
ISBN (Print)	9781538654286
DOIs	https://doi.org/10.23919/ACC.2018.8431113
State	Published - Aug 9 2018
Event	2018 Annual American Control Conference, ACC 2018 - Milwauke, United States Duration: Jun 27 2018 → Jun 29 2018

Publication series

Name	Proceedings of the American Control Conference
Volume	2018-June
ISSN (Print)	0743-1619

Other

Other	2018 Annual American Control Conference, ACC 2018
Country/Territory	United States
City	Milwauke
Period	6/27/18 → 6/29/18

Bibliographical note

Funding Information:
The work was supported by the National Science Foundation under Grant No. NSF-CMMI-1254129 entitled “CAREER: Probabilistic Tools for High Reliability Monitoring and Control of Wind Farms.” Peter Seiler is with the Aerospace Engineering and Mechanics Department, University of Minnesota, Email: seile017@umn.edu.

Publisher Copyright:
© 2018 AACC.

Access

10.23919/ACC.2018.8431113

OpenUrl availability

Full text

Cite this

An Iterative Algorithm to Estimate Invariant Sets for Uncertain Systems. / Seiler, Peter.
2018 Annual American Control Conference, ACC 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 4249-4254 8431113 (Proceedings of the American Control Conference; Vol. 2018-June).

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

Seiler, P 2018, An Iterative Algorithm to Estimate Invariant Sets for Uncertain Systems. in 2018 Annual American Control Conference, ACC 2018., 8431113, Proceedings of the American Control Conference, vol. 2018-June, Institute of Electrical and Electronics Engineers Inc., pp. 4249-4254, 2018 Annual American Control Conference, ACC 2018, Milwauke, United States, 6/27/18. https://doi.org/10.23919/ACC.2018.8431113

@inproceedings{33a3e58ca83c4c3092a67da2583ee099,

title = "An Iterative Algorithm to Estimate Invariant Sets for Uncertain Systems",

abstract = "This paper develops an iterative algorithm to estimate an invariant set for uncertain systems. The uncertain system is given as a connection of a nominal linear time-invariant system and a perturbation. The input/output behavior of the perturbation is described by integral quadratic constraints (IQCs). The proposed approach incorporates IQCs into a dissipation inequality formulation. One issue is that it is often useful to specify the IQC in the frequency domain or, equivalently, in the time-domain as a 'soft' infinite-horizon constraint. However, the dissipation inequality formulation requires constraints that are valid over all finite time horizons. The main technical result is a finite-horizon bound on soft IQCs constructed using a state-feedback transformation. This forms the basis for the proposed iterative algorithm to estimate invariant sets. A simple example is provided to demonstrate the proposed approach.",

author = "Peter Seiler",

note = "Funding Information: The work was supported by the National Science Foundation under Grant No. NSF-CMMI-1254129 entitled “CAREER: Probabilistic Tools for High Reliability Monitoring and Control of Wind Farms.” Peter Seiler is with the Aerospace Engineering and Mechanics Department, University of Minnesota, Email: seile017@umn.edu. Publisher Copyright: {\textcopyright} 2018 AACC.; 2018 Annual American Control Conference, ACC 2018 ; Conference date: 27-06-2018 Through 29-06-2018",

year = "2018",

month = aug,

day = "9",

doi = "10.23919/ACC.2018.8431113",

language = "English (US)",

isbn = "9781538654286",

series = "Proceedings of the American Control Conference",

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

pages = "4249--4254",

booktitle = "2018 Annual American Control Conference, ACC 2018",

}

TY - GEN

T1 - An Iterative Algorithm to Estimate Invariant Sets for Uncertain Systems

AU - Seiler, Peter

N1 - Funding Information: The work was supported by the National Science Foundation under Grant No. NSF-CMMI-1254129 entitled “CAREER: Probabilistic Tools for High Reliability Monitoring and Control of Wind Farms.” Peter Seiler is with the Aerospace Engineering and Mechanics Department, University of Minnesota, Email: seile017@umn.edu. Publisher Copyright: © 2018 AACC.

PY - 2018/8/9

Y1 - 2018/8/9

N2 - This paper develops an iterative algorithm to estimate an invariant set for uncertain systems. The uncertain system is given as a connection of a nominal linear time-invariant system and a perturbation. The input/output behavior of the perturbation is described by integral quadratic constraints (IQCs). The proposed approach incorporates IQCs into a dissipation inequality formulation. One issue is that it is often useful to specify the IQC in the frequency domain or, equivalently, in the time-domain as a 'soft' infinite-horizon constraint. However, the dissipation inequality formulation requires constraints that are valid over all finite time horizons. The main technical result is a finite-horizon bound on soft IQCs constructed using a state-feedback transformation. This forms the basis for the proposed iterative algorithm to estimate invariant sets. A simple example is provided to demonstrate the proposed approach.

AB - This paper develops an iterative algorithm to estimate an invariant set for uncertain systems. The uncertain system is given as a connection of a nominal linear time-invariant system and a perturbation. The input/output behavior of the perturbation is described by integral quadratic constraints (IQCs). The proposed approach incorporates IQCs into a dissipation inequality formulation. One issue is that it is often useful to specify the IQC in the frequency domain or, equivalently, in the time-domain as a 'soft' infinite-horizon constraint. However, the dissipation inequality formulation requires constraints that are valid over all finite time horizons. The main technical result is a finite-horizon bound on soft IQCs constructed using a state-feedback transformation. This forms the basis for the proposed iterative algorithm to estimate invariant sets. A simple example is provided to demonstrate the proposed approach.

UR - http://www.scopus.com/inward/record.url?scp=85052564117&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85052564117&partnerID=8YFLogxK

U2 - 10.23919/ACC.2018.8431113

DO - 10.23919/ACC.2018.8431113

M3 - Conference contribution

AN - SCOPUS:85052564117

SN - 9781538654286

T3 - Proceedings of the American Control Conference

SP - 4249

EP - 4254

BT - 2018 Annual American Control Conference, ACC 2018

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2018 Annual American Control Conference, ACC 2018

Y2 - 27 June 2018 through 29 June 2018

ER -

An Iterative Algorithm to Estimate Invariant Sets for Uncertain Systems

Abstract

Publication series

Other

Bibliographical note

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this