Computation of bifurcation margins based on robust control concepts

Iannelli, Andrea; Lowenberg, Mark; Marcos Esteban, Andrés

Publication:
Computation of bifurcation margins based on robust control concepts

dc.affiliation.dpto	UC3M. Departamento de Ingeniería Aeroespacial	es
dc.affiliation.grupoinv	UC3M. Grupo de Investigación: Equipo de Propulsión Espacial y Plasmas (EP2)	es
dc.contributor.author	Iannelli, Andrea
dc.contributor.author	Lowenberg, Mark
dc.contributor.author	Marcos Esteban, Andrés
dc.date.accessioned	2022-07-29T09:31:03Z
dc.date.available	2022-07-29T09:31:03Z
dc.date.issued	2020-08-25
dc.description.abstract	This article proposes a framework which allows the study of stability robustness of equilibria of a nonlinear system in the face of parametric uncertainties from the point of view of bifurcation theory. In this context, a branch of equilibria is stable if bifurcations (i.e., qualitative changes of the steady-state solutions) do not occur as one or more bifurcation parameters are varied. The work focuses specifically on Hopf bifurcations, where a stable branch of equilibria meets a branch of periodic solutions. It is of practical interest to evaluate how the presence of uncertain parameters in the system alters the result of analyses performed with respect to a nominal vector field. Note that in this article bifurcation parameters have a different meaning than uncertain parameters. To answer the question, the concept of robust bifurcation margins is proposed based on the idea of describing the uncertain system in a Linear Fractional Transformation fashion. The robust bifurcation margins can be interpreted as nonlinear analogues of the structural singular value, or µ, which provides robust stability margins for linear time invariant systems. Their computation is formulated as a nonlinear program aided by a continuation-based multistart strategy to mitigate the issue of local minima. Application of the framework is demonstrated on two case studies from the power system and aerospace literature.	en
dc.format.extent	36
dc.identifier.bibliographicCitation	Iannelli, A., Lowenberg, M., & Marcos, A. (2020). Computation of Bifurcation Margins Based on Robust Control Concepts. In SIAM Journal on Applied Dynamical Systems, 19(3), 1956–1992.	en
dc.identifier.doi	https://doi.org/10.1137/19m1303678
dc.identifier.issn	1536-0040
dc.identifier.publicationfirstpage	1956
dc.identifier.publicationissue	3
dc.identifier.publicationlastpage	1992
dc.identifier.publicationtitle	SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS	en
dc.identifier.publicationvolume	19
dc.identifier.uri	https://hdl.handle.net/10016/35563
dc.identifier.uxxi	AR/0000028015
dc.language.iso	eng	en
dc.publisher	Society for Industrial & Applied Mathematics (SIAM)	en
dc.relation.publisherversion	https://epubs.siam.org/doi/10.1137/19M1303678	en
dc.rights	© 2020, Society for Industrial and Applied Mathematics	en
dc.rights	Atribución 3.0 España	*
dc.rights.accessRights	open access	en
dc.rights.uri	http://creativecommons.org/licenses/by/3.0/es/	*
dc.subject.eciencia	Aeronáutica	es
dc.subject.other	Bifurcations	en
dc.subject.other	Numerical continuation	en
dc.subject.other	Robust control theory	en
dc.subject.other	Robust stability	en
dc.title	Computation of bifurcation margins based on robust control concepts	en
dc.type	research article	*
dc.type.hasVersion	AM	*
dspace.entity.type	Publication