Controllability of a Nonhomogeneous String and Ring under Time Dependent Tension

¹ University of Alaska Fairbanks, Fairbanks, AK 99775-6660, USA
² University of Tennessee at Chattanooga, 615 McCallie Avenue, Chattanooga, TN 37403-2598, USA
³ Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

^* Corresponding author. E-mail: ffsaa@uaf.edu

Abstract

We study controllability for a nonhomogeneous string and ring under an axial stretching tension that varies with time. We consider the boundary control for a string and distributed control for a ring. For a string, we are looking for a control f(t) ∈ L²(0, T) that drives the state solution to rest. We show that for a ring, two forces are required to achieve controllability. The controllability problem is reduced to a moment problem for the control. We describe the set of initial data which may be driven to rest by the control. The proof is based on an auxiliary basis property result.