Partial controllability of semilinear systems

Abstract

The paper considers semilinear control system in the product of Hilbert spaces X = H × G driven by densely defined closed linear operator A generating a strongly continuous semigroup. For the linear operator L, projecting X to H, it is proved a sufficient condition for L-partially exact controllability to L(D(A)) which means that for every initial state ξ ∈ X and every η ∈ D(A) there exists a control u such that Lxξ,u(T) = Lη, where x ξ,u is the state process corresponding the initial state ξ and the control u. The result is demonstrated on examples.