Sensitivity analysis of a bilinear optimal control problem

摘要

In this paper, we study the sensitivity of an optimal control problem of bilinear type. The cost is differentiable, strictly convex and quadratic. The system is governed by a fourth order parabolic operator and has an additive perturbation in the state equation, and a bilinear part with respect to the control $u$ and the state $z$ of the form $(u cdot abla ) z$. Under conditions of smallness of the initial state and perturbation, we exploit the properties of regularity and uniqueness of optimal control to demonstrate the stability of the optimal value function. The formula for directional derivatives at zero of the optimal value is explained.