Simultaneous controllability in sharp time for two elastic strings

¹ 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; avdonin@ist.flinders.edu.au.
³ Department of Mathematics, University of Nancy-I, BP. 239, 54506 Vandœuvre-lès-Nancy, France; Marius.Tucsnak@iecn.u-nancy.fr.

Received: 26 January 2000
Revised: 3 July 2000
Revised: 6 October 2000

Abstract

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.