The Kalman condition for the boundary controllability of coupled 1-d wave equations. (English) Zbl 1435.35397
Summary: The focus of this paper is the exact controllability of a system of \(N \) one-dimensional coupled wave equations when the control is exerted on a part of the boundary by means of one control. We give a Kalman condition (necessary and sufficient) and give a description of the attainable set. In general, this set is not optimal, but can be refined under certain conditions.
MSC:
| 35Q93 | PDEs in connection with control and optimization |
| 93B05 | Controllability |
| 93C20 | Control/observation systems governed by partial differential equations |
| 35L05 | Wave equation |
| 35P99 | Spectral theory and eigenvalue problems for partial differential equations |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
Keywords:
hyperbolic systems; wave equations; boundary controllability; Kalman rank condition; exponential divided differencesReferences:
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