Approximate Controllability of Semilinear Control System with State Delay Using Tikhonov Regularization

In this paper computation of control for an approximately controllable semilinear system with state delay is studied using Tikhonov regularization. Depending on the state delay occurred in the time interval, approximate controllability of the semilinear control system is proved under the assumption of approximate controllability of the corresponding linear system without state delay under some assumptions on the system constraints.Computing control for a given target state for the aforesaid system is ill-posed in the sense of Hadamard. Regularized control is computed using Tikhonov regularization for a given target state. Under some assumptions on system and nonlinear function f , it is proved that the target state corresponding to the regularized control is very close to the actual state to be attained by the system. Proposed Theory is corroborated with an example of diffusion system.