 Bang–bang control

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, also known as on-off control or two-position control, is a type of control strategy used in systems where precise control is not necessary or where a system can only operate in two states: fully "on" (maximum output) or fully "off" (minimum output). This approach is often applied in various engineering fields, including robotics, aerospace, and HVAC systems.