## Attainable Subspaces and the Bang-Bang Property of Time Optimal Controls for Heat Equations

- Gengsheng Wang, Yashan Xu, Yubiao Zhang
- SIAM J. Control and Optimization
- 2015

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@inproceedings{Mizel2007AnA, title={An abstract ‘ bang-bang principle ’ and time-optimal boundary control of the heat equation 1}, author={Victor J. Mizel and Thomas I. Seidman}, year={2007} }

- Published 2007

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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