Simultaneous controllability in sharp time for two elastic strings
Department of Applied Mathematics and Control, St. Petersburg State University,
St. Petersburg 198904, Russia.
2 Department of Mathematics and Statistics, The Flinders University of South Australia, P.O. Box 2100, Adelaide 5001, Australia; email@example.com.
3 Department of Mathematics, University of Nancy-I, BP. 239, 54506 Vandœuvre-lès-Nancy, France; Marius.Tucsnak@iecn.u-nancy.fr.
Revised: 3 July 2000
Revised: 6 October 2000
We study the simultaneously reachable subspace for two strings controlled from a common endpoint. We give necessary and sufficient conditions for simultaneous spectral and approximate controllability. Moreover we prove the lack of simultaneous exact controllability and we study the space of simultaneously reachable states as a function of the position of the joint. For each type of controllability result we give the sharp controllability time.
Mathematics Subject Classification: 93B / 35L / 42
Key words: Exact controllability / spectral controllability / approximate controllability / simultaneous controllability / string equation / boundary control / Riesz basis.
© EDP Sciences, SMAI, 2001