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Optimal control and the fibonacci sequence
Statistisk sentralbyrå.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Narvik University College, 8505 Narvik, Norway.
2012 (English)Report (Other academic)
Abstract [en]

We bridge mathematical number theory with that of 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.

Place, publisher, year, edition, pages
Oslo: Statistics Norway , 2012. , 33 p.
Keyword [en]
Mathematics, Information technology - Automatic control
Keyword [sv]
Fibonacci sequence, Optimal control, Matematik, Informationsteknik - Reglerteknik
Research subject
URN: urn:nbn:se:ltu:diva-24073Local ID: 99574a52-ca64-400b-a266-0156fab88c39OAI: diva2:997124
Godkänd; 2012; 20120118 (johanb)Available from: 2016-09-29 Created: 2016-09-29Bibliographically approved

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