Approximate Controllability of Semilinear Control System Using Tikhonov Regularization

Abstract

For an approximately controllable semilinear system, the problem of computing control for a given target state is converted into an equivalent problem of solving operator equation which is ill-posed. We exhibit a sequence of regularized controls which steers the semilinear control system from an arbitrary initial statex0to anϵneighbourhood of the target statexτat timeτ>0under the assumption that the nonlinear functionfis Lipschitz continuous. The convergence of the sequences of regularized controls and the corresponding mild solutions are shown under some assumptions on the system operators. It is also proved that the target state corresponding to the regularized control is close to the actual state to be attained.