An abstract ‘ bang-bang principle ’ and time-optimal boundary control of the heat equation 1

  title={An abstract ‘ bang-bang principle ’ and time-optimal boundary control of the heat equation 1},
  author={Victor J. Mizel and Thomas I. Seidman},
A principal technical result of this paper is that the onedimensional heat equation with boundary control is exactly null-controllable with control restricted to an arbitrary set E ⊂ [0, T ] of positive measure. A general abstract argument is presented to show that this implies the ‘bangbang’ property for time-optimal controls — i.e., such a control can take only extreme values of (the hull of) the constraint set — without imposing any condition regarding the target state, in contrast to… CONTINUE READING
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