PERTURBATIONS OF TIME OPTIMAL CONTROL PROBLEMS FOR PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS

This paper is addressed to a study of time optimal control problems for a family of systems governed by parabolic integro-differential equations. The target set is a closed ball centered at the origin of the state space and the control functions are distributed. We prove the optimal time and the associated optimal controls for the parabolic integro-differential equations, where the integral terms have a small perturbation and are close to those of the original problem for a parabolic equation. The method of the main result relies on the bang-bang property of optimal controls, the convergence of the associated minimization problems, and the connections between time optimal control problems and norm optimal control problems.