Optimal Control and the Fibonacci Sequence

Thomas Brasch (), Johan Byström () and Lars Petter Lystad ()
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Thomas Brasch: Statistics Norway
Johan Byström: Luleå University of Technology
Lars Petter Lystad: Narvik University College

Journal of Optimization Theory and Applications, 2012, vol. 154, issue 3, No 8, 857-878

Abstract: Abstract 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.

Keywords: Brock–Mirman model; Fibonacci sequence; Golden ratio; Mathematical number theory; Optimal control (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-012-0061-2

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