Optimal Control and the Fibonacci Sequence

@article{Brasch2012OptimalCA,
  title={Optimal Control and the Fibonacci Sequence},
  author={T. Brasch and J. Bystr{\"o}m and Lars Petter Lystad},
  journal={Journal of Optimization Theory and Applications},
  year={2012},
  volume={154},
  pages={857-878}
}
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… Expand
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