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Approximate Controllabilty of Semilinear Dynamic Equations on Time Scale

Abstract:

In this paper we study the approximate controllability of semilinear systems on time scale. In order to do so, we first give a complete characterization for the controllability of linear systems on time scale in terms of surjective linear operators in Hilbert spaces. Then we will prove that, under certain conditions on the nonlinear term, if the corresponding linear system is exactly controllable on [𝜏 − 𝛿, 𝜏]T, for any 𝛿 ∈ (0, 𝜏)T, then semilinear system on time scale is approximately controllable on [0, 𝜏]T.