Region of attraction analysis with Integral Quadratic Constraints

Andrea Iannelli; Peter Seiler; Andrés Marcos

doi:10.1016/j.automatica.2019.108543

Region of attraction analysis with Integral Quadratic Constraints

Andrea Iannelli, Peter Seiler, Andrés Marcos

Aerospace Engineering and Mechanics

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

15 Scopus citations

Abstract

A general framework is presented to estimate the Region of Attraction of attracting equilibrium points. The system is described by a feedback connection of a nonlinear (polynomial) system and a bounded operator. The input/output behavior of the operator is characterized using an Integral Quadratic Constraint. This allows to analyze generic problems including, for example, hard-nonlinearities and different classes of uncertainties, adding to the state of practice in the field which is typically limited to polynomial vector fields. The IQC description is also nonrestrictive, with the main result given for both hard and soft factorizations. Optimization algorithms based on Sum of Squares techniques are then proposed, with the aim to enlarge the inner estimates of the ROA. Numerical examples are provided to show the applicability of the approaches. These include a saturated plant where bounds on the states are exploited to refine the sector description, and a case study with parametric uncertainties for which the conservativeness of the results is reduced by using soft IQCs.

Original language	English (US)
Article number	108543
Journal	Automatica
Volume	109
DOIs	https://doi.org/10.1016/j.automatica.2019.108543
State	Published - Nov 2019

Bibliographical note

Funding Information:
The material in this paper was partially presented at the 57th IEEE Conference on Decision and Control, December 17?19, 2018, Miami Beach, Florida, USA. This work has received funding from the Horizon 2020 research and innovation framework programme under grant agreement No 636307, project FLEXOP. P. Seiler also acknowledges funding from the Hungarian Academy of Sciences, Institute for Computer Science and Control. This paper was recommended for publication in revised form by Associate Editor Denis Arzelier under the direction of Editor Richard Middleton ? The material in this paper was partially presented at the 57th IEEE Conference on Decision and Control, December 17?19, 2018, Miami Beach, Florida, USA. This work has received funding from the Horizon 2020 research and innovation framework programme under grant agreement No 636307, project FLEXOP. P. Seiler also acknowledges funding from the Hungarian Academy of Sciences, Institute for Computer Science and Control. This paper was recommended for publication in revised form by Associate Editor Denis Arzelier under the direction of Editor Richard Middleton The authors would like to thank the anonymous reviewers for their interesting remarks and insightful suggestions, which greatly contributed to improving the paper. ? The material in this paper was partially presented at the 57th IEEE Conference on Decision and Control, December 17?19, 2018, Miami Beach, Florida, USA. This work has received funding from the Horizon 2020 research and innovation framework programme under grant agreement No 636307, project FLEXOP. P. Seiler also acknowledges funding from the Hungarian Academy of Sciences, Institute for Computer Science and Control. This paper was recommended for publication in revised form by Associate Editor Denis Arzelier under the direction of Editor Richard Middleton

Publisher Copyright:
© 2019 Elsevier Ltd

Keywords

Dissipation inequality
Integral quadratic constraints
Local analysis
Nonlinear uncertain systems
Region of attraction

Publisher link

10.1016/j.automatica.2019.108543

Find It

Find It at U of M Libraries

Cite this

@article{a4efa037611648508570a9cf96d5f9dd,

title = "Region of attraction analysis with Integral Quadratic Constraints",

abstract = "A general framework is presented to estimate the Region of Attraction of attracting equilibrium points. The system is described by a feedback connection of a nonlinear (polynomial) system and a bounded operator. The input/output behavior of the operator is characterized using an Integral Quadratic Constraint. This allows to analyze generic problems including, for example, hard-nonlinearities and different classes of uncertainties, adding to the state of practice in the field which is typically limited to polynomial vector fields. The IQC description is also nonrestrictive, with the main result given for both hard and soft factorizations. Optimization algorithms based on Sum of Squares techniques are then proposed, with the aim to enlarge the inner estimates of the ROA. Numerical examples are provided to show the applicability of the approaches. These include a saturated plant where bounds on the states are exploited to refine the sector description, and a case study with parametric uncertainties for which the conservativeness of the results is reduced by using soft IQCs.",

keywords = "Dissipation inequality, Integral quadratic constraints, Local analysis, Nonlinear uncertain systems, Region of attraction",

author = "Andrea Iannelli and Peter Seiler and Andr{\'e}s Marcos",

note = "Funding Information: The material in this paper was partially presented at the 57th IEEE Conference on Decision and Control, December 17?19, 2018, Miami Beach, Florida, USA. This work has received funding from the Horizon 2020 research and innovation framework programme under grant agreement No 636307, project FLEXOP. P. Seiler also acknowledges funding from the Hungarian Academy of Sciences, Institute for Computer Science and Control. This paper was recommended for publication in revised form by Associate Editor Denis Arzelier under the direction of Editor Richard Middleton ? The material in this paper was partially presented at the 57th IEEE Conference on Decision and Control, December 17?19, 2018, Miami Beach, Florida, USA. This work has received funding from the Horizon 2020 research and innovation framework programme under grant agreement No 636307, project FLEXOP. P. Seiler also acknowledges funding from the Hungarian Academy of Sciences, Institute for Computer Science and Control. This paper was recommended for publication in revised form by Associate Editor Denis Arzelier under the direction of Editor Richard Middleton The authors would like to thank the anonymous reviewers for their interesting remarks and insightful suggestions, which greatly contributed to improving the paper. ? The material in this paper was partially presented at the 57th IEEE Conference on Decision and Control, December 17?19, 2018, Miami Beach, Florida, USA. This work has received funding from the Horizon 2020 research and innovation framework programme under grant agreement No 636307, project FLEXOP. P. Seiler also acknowledges funding from the Hungarian Academy of Sciences, Institute for Computer Science and Control. This paper was recommended for publication in revised form by Associate Editor Denis Arzelier under the direction of Editor Richard Middleton Publisher Copyright: {\textcopyright} 2019 Elsevier Ltd",

year = "2019",

month = nov,

doi = "10.1016/j.automatica.2019.108543",

language = "English (US)",

volume = "109",

journal = "Automatica",

issn = "0005-1098",

publisher = "Elsevier Limited",

}

TY - JOUR

T1 - Region of attraction analysis with Integral Quadratic Constraints

AU - Iannelli, Andrea

AU - Seiler, Peter

AU - Marcos, Andrés

N1 - Funding Information: The material in this paper was partially presented at the 57th IEEE Conference on Decision and Control, December 17?19, 2018, Miami Beach, Florida, USA. This work has received funding from the Horizon 2020 research and innovation framework programme under grant agreement No 636307, project FLEXOP. P. Seiler also acknowledges funding from the Hungarian Academy of Sciences, Institute for Computer Science and Control. This paper was recommended for publication in revised form by Associate Editor Denis Arzelier under the direction of Editor Richard Middleton ? The material in this paper was partially presented at the 57th IEEE Conference on Decision and Control, December 17?19, 2018, Miami Beach, Florida, USA. This work has received funding from the Horizon 2020 research and innovation framework programme under grant agreement No 636307, project FLEXOP. P. Seiler also acknowledges funding from the Hungarian Academy of Sciences, Institute for Computer Science and Control. This paper was recommended for publication in revised form by Associate Editor Denis Arzelier under the direction of Editor Richard Middleton The authors would like to thank the anonymous reviewers for their interesting remarks and insightful suggestions, which greatly contributed to improving the paper. ? The material in this paper was partially presented at the 57th IEEE Conference on Decision and Control, December 17?19, 2018, Miami Beach, Florida, USA. This work has received funding from the Horizon 2020 research and innovation framework programme under grant agreement No 636307, project FLEXOP. P. Seiler also acknowledges funding from the Hungarian Academy of Sciences, Institute for Computer Science and Control. This paper was recommended for publication in revised form by Associate Editor Denis Arzelier under the direction of Editor Richard Middleton Publisher Copyright: © 2019 Elsevier Ltd

PY - 2019/11

Y1 - 2019/11

N2 - A general framework is presented to estimate the Region of Attraction of attracting equilibrium points. The system is described by a feedback connection of a nonlinear (polynomial) system and a bounded operator. The input/output behavior of the operator is characterized using an Integral Quadratic Constraint. This allows to analyze generic problems including, for example, hard-nonlinearities and different classes of uncertainties, adding to the state of practice in the field which is typically limited to polynomial vector fields. The IQC description is also nonrestrictive, with the main result given for both hard and soft factorizations. Optimization algorithms based on Sum of Squares techniques are then proposed, with the aim to enlarge the inner estimates of the ROA. Numerical examples are provided to show the applicability of the approaches. These include a saturated plant where bounds on the states are exploited to refine the sector description, and a case study with parametric uncertainties for which the conservativeness of the results is reduced by using soft IQCs.

AB - A general framework is presented to estimate the Region of Attraction of attracting equilibrium points. The system is described by a feedback connection of a nonlinear (polynomial) system and a bounded operator. The input/output behavior of the operator is characterized using an Integral Quadratic Constraint. This allows to analyze generic problems including, for example, hard-nonlinearities and different classes of uncertainties, adding to the state of practice in the field which is typically limited to polynomial vector fields. The IQC description is also nonrestrictive, with the main result given for both hard and soft factorizations. Optimization algorithms based on Sum of Squares techniques are then proposed, with the aim to enlarge the inner estimates of the ROA. Numerical examples are provided to show the applicability of the approaches. These include a saturated plant where bounds on the states are exploited to refine the sector description, and a case study with parametric uncertainties for which the conservativeness of the results is reduced by using soft IQCs.

KW - Dissipation inequality

KW - Integral quadratic constraints

KW - Local analysis

KW - Nonlinear uncertain systems

KW - Region of attraction

UR - http://www.scopus.com/inward/record.url?scp=85071325457&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85071325457&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2019.108543

DO - 10.1016/j.automatica.2019.108543

M3 - Article

AN - SCOPUS:85071325457

SN - 0005-1098

VL - 109

JO - Automatica

JF - Automatica

M1 - 108543

ER -

Region of attraction analysis with Integral Quadratic Constraints

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this