Abstract
This paper discusses optimal periodic control problems for quasilinear systems in Hilbert spaces. Using Ekeland’s variational principle, a global maximum principle is proven.
Then the question of local properness is discussed, i.e. if an optimal steady state can be improved by allowing proper periodic controls and trajectories. This discussion is based on second order necessary optimality conditions obtained from general optimization theory in Banach spaces.
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© 1987 Springer Basel AG
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Colonius, F. (1987). Optimal Periodic Control of Quasilinear Systems in Hilbert Spaces. In: Hoffmann, KH., Krabs, W. (eds) Optimal Control of Partial Differential Equations II: Theory and Applications. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 78. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7627-8_4
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DOI: https://doi.org/10.1007/978-3-0348-7627-8_4
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7629-2
Online ISBN: 978-3-0348-7627-8
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