Manifold turnpikes, trims, and symmetries

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dc.contributor.authorFaulwasser, Timm
dc.contributor.authorFlaßkamp, Kathrin
dc.contributor.authorOber-Blöbaum, Sina
dc.contributor.authorSchaller, Manuel
dc.contributor.authorWorthmann, Karl
dc.date.accessioned2023-06-20T13:31:34Z
dc.date.available2023-06-20T13:31:34Z
dc.date.issued2022-05-03
dc.description.abstractClassical turnpikes correspond to optimal steady states which are attractors of infinite-horizon optimal control problems. In this paper, motivated by mechanical systems with symmetries, we generalize this concept to manifold turnpikes. Specifically, the necessary optimality conditions projected onto a symmetry-induced manifold coincide with those of a reduced-order problem defined on the manifold under certain conditions. We also propose sufficient conditions for the existence of manifold turnpikes based on a tailored notion of dissipativity with respect to manifolds. Furthermore, we show how the classical Legendre transformation between Euler–Lagrange and Hamilton formalisms can be extended to the adjoint variables. Finally, we draw upon the Kepler problem to illustrate our findings.en
dc.identifier.urihttp://hdl.handle.net/2003/41829
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-23673
dc.language.isoende
dc.relation.ispartofseriesMathematics of control, signals, and systems;34(4)
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/de
dc.subjectTurnpikesen
dc.subjectGeometric controlen
dc.subjectMotion primitivesen
dc.subjectOptimal controlen
dc.subjectSymmetryen
dc.subjectDissipativityen
dc.subject.ddc620
dc.titleManifold turnpikes, trims, and symmetriesen
dc.typeTextde
dc.type.publicationtypeArticlede
dcterms.accessRightsopen access
eldorado.secondarypublicationtruede
eldorado.secondarypublication.primarycitationFaulwasser, T., Flaßkamp, K., Ober-Blöbaum, S. et al. Manifold turnpikes, trims, and symmetries. Math. Control Signals Syst. 34, 759–788 (2022). https://doi.org/10.1007/s00498-022-00321-6de
eldorado.secondarypublication.primaryidentifierhttps://doi.org/10.1007/s00498-022-00321-6de

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