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Optimal control and the Fibonacci sequence

Brasch, Thomas von; Byström, Johan; Lystad, Lars Petter
Journal article, Peer reviewed
Accepted version
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Journal of Optimization_Brasch_artikkel.pdf (425.0Kb)
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http://hdl.handle.net/11250/2580549
Utgivelsesdato
2012-04-26
Metadata
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  • Artikler / Journal articles [372]
Originalversjon
Brasch, T. von, Byström, J. & Lystad, L.P. Journal of Optimization Theory and Application (2012) 154: 857. https://doi.org/10.1007/s10957-012-0061-2   https://doi.org/10.1007/s10957-012-0061-2
Sammendrag
We bridge mathematical number theory with optimal control and show that a generalised Fibonacci sequence enters the control function of finite-horizon dynamic optimisation problems with one state and one control variable. In particular, we show that the recursive expression describing the first-order approximation of the control function can be written in terms of a generalised Fibonacci sequence when restricting the final state to equal the steady-state of the system. Further, by deriving the solution to this sequence, we are able to write the first-order approximation of optimal control explicitly. Our procedure is illustrated in an example often referred to as the Brock–Mirman economic growth model.
Utgiver
Springer
Tidsskrift
Journal of Optimization Theory and Applications
Opphavsrett
© Springer Science+Business Media, LLC 2012

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