Scientific article
Published:
Optimal Control and the Fibonacci Sequence
Written by
Thomas Rolf Lydersen Lystad von Brasch
Johan Byström
Lars Petter Lystad
Ed.
Summary:
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
Written by
Thomas Rolf Lydersen Lystad von Brasch
Johan Byström
Lars Petter Lystad