Optimal Control for non–isothermal crystallization of polymers

In this paper an optimal control problem for polymer crystallization is investigated. The crystallization is described by a non–isothermal Avrami–Kolmogorov model. The boundary temperature serves as control variable. The cost functional takes the spatial variation of the crystallinity and the final degree of crystallization into account. The resulting boundary control problem for a parabolic equation coupled with two ordinary differential equations is treated by an adjoint variable approach. A steepest descent algorithm is used to solve the problem numerically. Simulations illustrate the applicability and performance of the optimization algorithm.