Sensitivity Analysis of Optimal Control Parabolic Systems with Retardations

Abstract

The first order sensitivity analysis is performed for a class of optimal control problems for time lag parabolic equations in which retarded arguments appear in the integral form with h ∈ (0, b) in the state equations and with k ∈ (0, c) in the Neumann boundary conditions. The optimality system is analyzed with the respect to a small parameter. The directional derivative of the optimal control is obtained as a solution to an auxiliary optimization problem. The control constraints for the auxilary optimization problem are received.