Optimal control of sterilization of prepackaged food in the case of problem with free final time and phase constraints

This paper is concerned with the optimal control of the sterilization of prepackaged food. The investigated system is constructed as an optimal control problem with free final horizon and phase constraints. Pontryagin's maximum principle, the necessary optimality condition for the system, is studied by the Dubovitskii and Milyutin functional analytical approach. The derived necessary condition is presented for the problem with both the control constraints and the state constraints.