Robust estimations of the Region of Attraction using invariant sets

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Show simple item record Iannelli, Andrea Marcos Esteban, Andrés Lowenberg, Mark 2022-07-20T08:36:48Z 2022-07-20T08:36:48Z 2019-05
dc.identifier.bibliographicCitation Iannelli, A., Marcos, A., & Lowenberg, M. (2019). Robust estimations of the Region of Attraction using invariant sets. In Journal of the Franklin Institute, 356(8), 4622–4647
dc.identifier.issn 0016-0032
dc.description.abstract The Region of Attraction of an equilibrium point is the set of initial conditions whose trajectories converge to it asymptotically. This article, building on a recent work on positively invariant sets, deals with inner estimates of the ROA of polynomial nonlinear dynamics. The problem is solved numerically by means of Sum Of Squares relaxations, which allow set containment conditions to be enforced. Numerical issues related to the ensuing optimization are discussed and strategies to tackle them are proposed. These range from the adoption of different iterative methods to the reduction of the polynomial variables involved in the optimization. The main contribution of the work is an algorithm to perform the ROA calculation for systems subject to modeling uncertainties, and its applicability is showcased with two case studies of increasing complexity. Results, for both nominal and uncertain systems, are compared with a standard algorithm from the literature based on Lyapunov function level sets. They confirm the advantages in adopting the invariant sets approach, and show that as the size of the system and the number of uncertainty increase, the proposed heuristics ameliorate the commented numerical issues.
dc.description.sponsorship This work has received funding from the Horizon 2020 research and innovation programme under grant agreement No 636307, project FLEXOP. The authors would like to thank Prof. Pete Seiler for helpful discussions about ROA and SOS.
dc.format.extent 25
dc.language.iso eng
dc.publisher ELSEVIER BV
dc.rights © 2019 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.subject.other Region of attraction
dc.subject.other Robust analysis
dc.subject.other Nonlinear dynamics
dc.subject.other Sum of squares
dc.subject.other Uncertainties
dc.subject.other Local analysis
dc.title Robust estimations of the Region of Attraction using invariant sets
dc.type article
dc.subject.eciencia Aeronáutica
dc.rights.accessRights openAccess
dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/636307
dc.type.version submittedVersion
dc.identifier.publicationfirstpage 4622
dc.identifier.publicationissue 8
dc.identifier.publicationlastpage 4647
dc.identifier.publicationvolume 356
dc.identifier.uxxi AR/0000028008
dc.contributor.funder European Commission
dc.affiliation.dpto UC3M. Departamento de Ingeniería Aeroespacial
dc.affiliation.grupoinv UC3M. Grupo de Investigación: Equipo de Propulsión Espacial y Plasmas (EP2)
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