Authors: Faulwasser, Timm
Flaßkamp, Kathrin
Ober-Blöbaum, Sina
Schaller, Manuel
Worthmann, Karl
Title: Manifold turnpikes, trims, and symmetries
Language (ISO): en
Abstract: Classical 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.
Subject Headings: Turnpikes
Geometric control
Motion primitives
Optimal control
Issue Date: 2022-05-03
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Appears in Collections:Sonstige Veröffentlichungen (Institut für Energiesysteme, Energieeffizienz und Energiewirtschaft)

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