On boundary controllability of one-dimensional vibrating systems by W, p-controls for p ∈ [2, ∞]

✍ Scribed by W. Krabs; G. Leugering

• Publisher: John Wiley and Sons
• Year: 1994
• Tongue: English
• Weight: 679 KB
• Volume: 17
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1670170202

✦ Synopsis

Abstract

This paper is concerned with boundary control of one‐dimensional vibrating media whose motion is governed by a wave equation with a 2__n__‐order spatial self‐adjoint and positive‐definite linear differential operator with respect to 2__n__ boundary conditions. Control is applied to one of the boundary conditions and the control function is allowed to vary in the Sobolev space W, ^p^ for p∈[2, ∞] With the aid of Banach space theory of trigonometric moment problems, necessary and sufficient conditions for null‐controllability are derived and applied to vibrating strings and Euler beams.

For vibrating strings also, null‐controllability by L^p^‐controls on the boundary is shown by a direct method which makes use of d'Alembert's solution formula for the wave equation.