Finite-dimensional boundary control of underactuated heat-heat cascades
Résumé
This paper addresses the problem of output feedback stabilization of a cascade of two underactuated heat equations that are coupled in the boundary conditions. The input is a boundary control for the first component of the cascade while the output is made on the second component of the cascade. The key idea developed in this paper is to carry out spectral reductions, not for each of the two components of the cascade separately, but instead, directly for the PDE cascade viewed as one single system. A detailed study of the eigenelements of the PDE cascade yields a complete and explicit characterization of modal controllability and observability properties. This enables the derivation of an explicit output feedback control strategy for the exponential stabilization of the plant.
Domaines
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