Pontryagin's maximum principle for optimal control of an extrusion process

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.