On the boundary controllability of first-order hyperbolic systems

Abstract

We discuss some results concerning the boundary controllability and stabilizability of a hyperbolic system of conservation laws ∂ u ∂ t + ∂ f ( u ) ∂ x = 0 , t ⩾ 0 , x ∈ ] 0 , 1 [ , where we regard the boundary data (or a partial number of their components) as boundary input controls. In particular, we consider the problem of the global exact boundary controllability of a first order linear hyperbolic system with constant coefficients relative to the linear boundary conditions. Under generic orthogonality assumptions on the boundary and control matrices, and assuming a non-resonance condition of the characteristic speeds we show that one can steer in finite time the solution from any initial condition ϕ ∈ L 1 , to any terminal state ψ ∈ L 1 , even in the case where only a partial control of the boundary values is available.