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

@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}
}
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
Highly Cited
This paper has 34 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 22 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 13 references

The ‘bang-bang’ principle for the time-optimal problem in boundary control of the heat equation

  • E.J.P.G. Schmidt
  • SIAM J. Control Optim. 18, pp. 101–107
  • 1980
Highly Influential
4 Excerpts

Time-invariance of the reachable set for linear control problems

  • T. I. Seidman
  • J. Math. Anal. Appl. 72, pp. 17–20
  • 1979
Highly Influential
4 Excerpts

Contrôle exact de l’équation de la chaleur

  • G. Lebeau, L. Robbiano
  • Comm. P.D.E, 20, pp. 335-356,
  • 1995
1 Excerpt

On Moment Theory and Controllability of One-Dimensional Vibrating Systems and Heating Processes (Lecture Notes in Control and Inf

  • W. Krabs
  • Sci. #173), Springer-Verlag, New York
  • 1992
3 Excerpts

Un contre-exemple en théorie de la commande en temps minimal des systèmes paraboliques

  • J. Henry
  • C.R. Acad. Sci. Paris (série A) 289, pp. 87–89
  • 1979
1 Excerpt

Vector Measures and Control Systems

  • I. Kluvanek, G. Knowles
  • (Mathematics Studies #20), North-Holland
  • 1975
1 Excerpt

Non-Homogeneous Boundary Value Problems and Applications

  • J. L. Lions, E. Magenes
  • vol. II, Springer-Verlag, Berlin
  • 1972
1 Excerpt

Similar Papers

Loading similar papers…