Are bang-bang minimum-time control policies evolutionarily inevitable?

The extent to which minimum-time control policies are necessarily bang-bang is investigated. It is shown that this very important issue can be conveniently examined by means of genetic algorithms. These general results are illustrated by the genetic design of a minimum-time controller for a second-order plant. It transpires that the control policies generated by a two-level hierarchy of genetic algorithms evolve towards a bang-bang form as the performance of the associated controller evolves towards time-optimality