Bang-bang control
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In optimal control problems, it is sometimes the case that a control is restricted to be between a lower and an upper bound. If the optimal control switches from one extreme to the other at certain times (i.e. is never strictly in between the bounds) then the control is referred to as a bang-bang control or a bang-bang solution.
Bang-bang controls frequently arise in minimum time problems. For example if it is desired to stop a car in the shortest possible time after a traffic light turns red, the solution is to apply maximum braking as soon as the light changes. This solution (a rather uncomfortable one for the passengers) is a bang-bang solution: no braking followed by maximum braking. Such solutions also arise when the Hamiltonian is linear in the control variable; application of Pontryagin's minimum principle will then lead to pushing the control to its upper or lower bound depending on the sign of the coefficient of u in the Hamiltonian.
