We discuss some results concerning the boundary controllability and stabilizability of a hyperbolic system of conservation laws $$ \frac{\partial u}{\partial t}+\frac{\partial f(u)}{\partial x}=0, \qquad\ t\geq 0,~x\in\,]0,1[, $$ 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 $\vfi\in L^1$ to any terminal state $\psi\in L^1$ even in the case where only a partial control of the boundary values is available.
On the boundary controllability of first order hyperbolic systems
ANCONA, FABIO;
2005
Abstract
We discuss some results concerning the boundary controllability and stabilizability of a hyperbolic system of conservation laws $$ \frac{\partial u}{\partial t}+\frac{\partial f(u)}{\partial x}=0, \qquad\ t\geq 0,~x\in\,]0,1[, $$ 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 $\vfi\in L^1$ to any terminal state $\psi\in L^1$ even in the case where only a partial control of the boundary values is available.Pubblicazioni consigliate
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