ON BOUNDARY CONTROLLABILITY OF ONE-DIMENSIONAL VIBRATING SYSTEMS BY W(0)1,P-CONTROLS FOR P-IS-AN-ELEMENT-OF[2, INFINITY]

This paper is concerned with boundary control of one-dimensional vibra ting media whose motion is governed by a wave equation with a 2n-order spatial self-adjoint and positive-definite linear differential operat or with respect to 2n boundary conditions. Control is applied to one o f the boundary conditions and the control function is allowed to vary in the Sobolev space W-0(1.p) for p is-an-element-of [2, infinity]. Wi th the aid of Banach space theory of trigonometric moment problems, ne cessary and sufficient conditions for null-controllability are derived and applied to vibrating strings and Euler beams. For vibrating strin gs also, null-controllability by L(p)-controls on the boundary is show n by a direct method which makes use of d'Alembert's solution formula for the wave equation.