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

Andrea Iannelli, Andres Marcos, Peter J Seiler Jr

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages725-730
Number of pages6
ISBN (Electronic)9781538613955
DOIs
StatePublished - Jan 18 2019
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December
ISSN (Print)0743-1546

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
CountryUnited States
CityMiami
Period12/17/1812/19/18

Fingerprint

Branch
Uncertainty
Point Location
Formulation
Dependent
Stability Region
Local Stability
Sum of squares
Steady-state Solution
Independent Set
Equilibrium Point
Level Set
Numerical Examples
Estimate
Range of data

Cite this

Iannelli, A., Marcos, A., & Seiler Jr, P. J. (2019). An equilibrium-independent region of attraction formulation for systems with uncertainty-dependent equilibria. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 725-730). [8619153] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. 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 Jr, Peter J.

2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. p. 725-730 8619153 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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