A <control input> taking only extreme admissible values except possibly on a switching or singular set. If the <Hamiltonian of an optimal-control problem> is affine in a scalar control $u\in[0,1]$, a nonzero coefficient selects $u=0$ or $u=1$; a zero coefficient does not determine the control.


Bang-bang control

Choice of a <control input> to minimize an objective subject to <differential equations> for a state and constraints on the control, state or terminal time. Necessary conditions such as the <Pontryagin maximum principle> require regularity hypotheses and do not by themselves prove global optimality.


Optimal control

{title2=$u(t)$}

A chosen input to a dynamical system, commonly written $u(t)$ in the state equation $\dot x=f(t,x,u)$. An <optimal control> problem specifies both the admissible input set and any information or regularity constraints on the choice.


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 Incoming links: Control input