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Manifold turnpikes, trims, and symmetries
Citation Link: https://doi.org/10.15480/882.9185
Publikationstyp
Journal Article
Date Issued
2022-12
Sprache
English
Author(s)
TORE-DOI
Volume
34
Issue
4
Start Page
759
End Page
788
Citation
Mathematics of Control, Signals, and Systems 34 (4): 759-788 (2022-01)
Publisher DOI
Scopus ID
Publisher
Springer
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.
Subjects
Dissipativity
Geometric control
Motion primitives
Optimal control
Symmetry
Turnpikes
DDC Class
621: Applied Physics
510: Mathematics
Publication version
publishedVersion
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s00498-022-00321-6.pdf
Type
Main Article
Size
1.1 MB
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