An equilibrium-independent region of attraction formulation for systems with uncertainty-dependent equilibria

Andrea Iannelli; Andres Marcos; Peter Seiler

doi:10.1109/CDC.2018.8619153

An equilibrium-independent region of attraction formulation for systems with uncertainty-dependent equilibria

Andrea Iannelli, Andres Marcos, Peter Seiler

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

7 Citations (Scopus)

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Abstract

This paper aims to compute the region of attraction (ROA) of equilibrium points whose location is modified by the uncertainties. The local stability region is formulated as an equilibrium-independent level set by restricting the attention to contractive functions which do not explicitly depend on the equilibrium. Another favourable feature of the approach is that it can be applied to systems having one or more branches of steady-state solutions (e.g. multistable systems). Inner estimates of the ROA are numerically computed by means of Sum of Square techniques, which allow to specify the allowed uncertainty range and the analyzed branch as set containment conditions, resulting in a compact and flexible formulation. A numerical example shows the application of the method and highlights its peculiar features.

Original language	English
Title of host publication	2018 IEEE Conference on Decision and Control, CDC 2018
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	725-730
Number of pages	6
Volume	2018-December
ISBN (Electronic)	9781538613955
ISBN (Print)	9781538613962
DOIs	https://doi.org/10.1109/CDC.2018.8619153
Publication status	Published - 21 Jan 2019
Event	57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: 17 Dec 2018 → 19 Dec 2018

Publication series

Name
ISSN (Print)	0743-1546

Conference

Conference	57th IEEE Conference on Decision and Control, CDC 2018
Country/Territory	United States
City	Miami
Period	17/12/18 → 19/12/18

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10.1109/CDC.2018.8619153

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title = "An equilibrium-independent region of attraction formulation for systems with uncertainty-dependent equilibria",

abstract = "This paper aims to compute the region of attraction (ROA) of equilibrium points whose location is modified by the uncertainties. The local stability region is formulated as an equilibrium-independent level set by restricting the attention to contractive functions which do not explicitly depend on the equilibrium. Another favourable feature of the approach is that it can be applied to systems having one or more branches of steady-state solutions (e.g. multistable systems). Inner estimates of the ROA are numerically computed by means of Sum of Square techniques, which allow to specify the allowed uncertainty range and the analyzed branch as set containment conditions, resulting in a compact and flexible formulation. A numerical example shows the application of the method and highlights its peculiar features.",

author = "Andrea Iannelli and Andres Marcos and Peter Seiler",

year = "2019",

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doi = "10.1109/CDC.2018.8619153",

language = "English",

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volume = "2018-December",

publisher = "Institute of Electrical and Electronics Engineers (IEEE)",

pages = "725--730",

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note = "57th IEEE Conference on Decision and Control, CDC 2018 ; Conference date: 17-12-2018 Through 19-12-2018",

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Iannelli, A, Marcos, A & Seiler, P 2019, An equilibrium-independent region of attraction formulation for systems with uncertainty-dependent equilibria. in 2018 IEEE Conference on Decision and Control, CDC 2018. vol. 2018-December, 8619153, Institute of Electrical and Electronics Engineers (IEEE), pp. 725-730, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 17/12/18. https://doi.org/10.1109/CDC.2018.8619153

An equilibrium-independent region of attraction formulation for systems with uncertainty-dependent equilibria. / Iannelli, Andrea; Marcos, Andres; Seiler, Peter.
2018 IEEE Conference on Decision and Control, CDC 2018. Vol. 2018-December Institute of Electrical and Electronics Engineers (IEEE), 2019. p. 725-730 8619153.

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

TY - GEN

T1 - An equilibrium-independent region of attraction formulation for systems with uncertainty-dependent equilibria

AU - Iannelli, Andrea

AU - Marcos, Andres

AU - Seiler, Peter

PY - 2019/1/21

Y1 - 2019/1/21

N2 - This paper aims to compute the region of attraction (ROA) of equilibrium points whose location is modified by the uncertainties. The local stability region is formulated as an equilibrium-independent level set by restricting the attention to contractive functions which do not explicitly depend on the equilibrium. Another favourable feature of the approach is that it can be applied to systems having one or more branches of steady-state solutions (e.g. multistable systems). Inner estimates of the ROA are numerically computed by means of Sum of Square techniques, which allow to specify the allowed uncertainty range and the analyzed branch as set containment conditions, resulting in a compact and flexible formulation. A numerical example shows the application of the method and highlights its peculiar features.

AB - This paper aims to compute the region of attraction (ROA) of equilibrium points whose location is modified by the uncertainties. The local stability region is formulated as an equilibrium-independent level set by restricting the attention to contractive functions which do not explicitly depend on the equilibrium. Another favourable feature of the approach is that it can be applied to systems having one or more branches of steady-state solutions (e.g. multistable systems). Inner estimates of the ROA are numerically computed by means of Sum of Square techniques, which allow to specify the allowed uncertainty range and the analyzed branch as set containment conditions, resulting in a compact and flexible formulation. A numerical example shows the application of the method and highlights its peculiar features.

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SN - 9781538613962

VL - 2018-December

SP - 725

EP - 730

BT - 2018 IEEE Conference on Decision and Control, CDC 2018

PB - Institute of Electrical and Electronics Engineers (IEEE)

T2 - 57th IEEE Conference on Decision and Control, CDC 2018

Y2 - 17 December 2018 through 19 December 2018

ER -

An equilibrium-independent region of attraction formulation for systems with uncertainty-dependent equilibria

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