Exact boundary controllability of a coupled system

Exact boundary controllability of coupled hyperbolic equations

We study the exact boundary controllability of two coupled one dimensional wave equations with a control acting only in one equation. The problem is transformed into a moment problem. This framework has been used in control theory of distributed parameter systems since the classical works of A.G. Butkovsky, H.O. Fattorini and D.L. Russell in the late 1960s to the early 1970s. We use recent resu...

Exact controllability of a system of coupled strings in parallel

Boundary controllability of a coupled wave/Kirchoff system

We consider two problems in boundary controllability of coupled wave/Kirchoff systems. Let Ω be a bounded region in R, n ≥ 2, with Lipschitz continuous boundary Γ. In the motivating structural acoustics application, Ω represents an acoustic cavity. Let Γ0 be a flat subset of Γ which represents a flexible wall of the cavity. Let z denote the acoustic velocity potential, which satisfies a wave eq...

Exact boundary controllability of a Rao-Nakra sandwich beam

We consider a three layer Rao-Nakra sandwich beam with damping proportional to shear included in the core layer. We prove that eigenvectors of the beam form a Riesz basis for the natural energy space. In the damped case, we are able to give precise conditions under which solutions decay at a uniform exponential rate. We also consider the problem of boundary control using bending moment and late...

Exact Boundary Controllability of a System of Mixed Order with Essential Spectrum

We address in this work the exact boundary controllability of a linear hyperbolic system of the form u′′+Au = 0 with u = (u1, u2) T posed in (0, T )× (0, 1). A denotes a self-adjoint operator of mixed order that usually appears in the modelization of a linear elastic membrane shell. The operator A possesses an essential spectrum which prevents the exact controllability from holding uniformly wi...