Abstract
In this paper we consider a class of bi-level optimal control problems. Both the upper and lower level problems are formulated as ordinary optimal control models of Lagrange type. Our goal is to formulate and prove a general existence theorem for an optimal solution based on classical compactness, convexity and seminormality conditions originating in the work of L. Tonelli for ordinary calculus of variations problems and extended to optimal control problems by L. Cesari, R.T. Rockafellar, L. Berkovitz and others. A distinguishing feature of our result is that we do not require the lower level problem to have a unique optimal solution corresponding to each admissible strategy of the upper level problem.
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References
Cesari L (1983) Optimization-theory and applications: problems with ordinary differential equations. In: Applications of applied mathematics, vol 17. Springer, New York
Dunford N, Schwartz JT (1958) Linear operators. I. General theory. In: Pure and applied mathematics, vol 7. Interscience Publishers, New York, with the assistance of W.G. Bade and R.G. Bartle
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Carlson, D.A. (2013). Existence of Optimal Controls for a Bi-Level Optimal Control Problem. In: Křivan, V., Zaccour, G. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 13. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-02690-9_4
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DOI: https://doi.org/10.1007/978-3-319-02690-9_4
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-02689-3
Online ISBN: 978-3-319-02690-9
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