Processi di controllo con parametri distribuiti in insiemi non limitati. Controllabilità con luogo iniziale variabile
We study the controllability with variable initial locus of some distributed parameter linear control system.In this setting, we study the controllability of such system from a given initial state, to be attained on the variable initial locus, to an arbitrary final state, to be attained on the fixed final locus l(a, b).
We consider both exact and approximate controllability. We get a characterization of the approximate controllability when the set of the available controls is the unit ball of L^q (L I, J , Rm ), q ≥ p. Also, assuming a suitable invertibility property for the matrix F , we show a necessary and sufficient condition for the exact controllability when a larger set of available controls is considered. Finally, we study the permanence of both controllability properties with respect to changes of the fixed final locus l(a, b).
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