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Publisert:

Optimal Control and the Fibonacci Sequence

Skrevet av

Thomas Rolf Lydersen Lystad von Brasch
Johan Byström
Lars Petter Lystad

Red.

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.
  • Published year: 2012
  • DOI: 10.1007/s10957-012-0061-2
  • Language: Engelsk
  • Pages: 857 - 878
  • Volume: 154
  • Booklet: 3
  • Journal: Journal of Optimization Theory and Applications

Skrevet av

Thomas Rolf Lydersen Lystad von Brasch
Johan Byström
Lars Petter Lystad