In this article, two optimal control problems of an extrusion process are considered in the isothermal case. The controlled system consists of a hyperbolic partial differential equation coupled with a nonlinear ordinary differential equation. Equipped with two control variables, the system describes the evolution of a moving interface between a fully filled zone and a partially filled zone. The Dubovitskii and Milyutin functional analytical approach is adopted in the investigation of the Pontryagin maximum principle for the optimal control problem. In both fixed and free final horizon cases, the corresponding necessary optimality conditions are, respectively, established. A remark is then made for illustrating the applicability of the obtained results.

在本文中，在等温情况下考虑了挤出过程的两个最优控制问题。受控系统由一个双曲偏微分方程和一个非线性常微分方程组成。该系统配备了两个控制变量，描述了完全填充区域和部分填充区域之间移动界面的演变。Dubovitskii 和 Milyutin 泛函分析方法用于研究最优控制问题的 Pontryagin 最大值原理。在固定和自由最终时域情况下，分别建立了相应的必要最优条件。然后进行评论以说明所得结果的适用性。