Maximum principle for optimal control of sterilization of prepackaged food

In the food industry field, heat sterilization, as a routine sterilization approach, is widely adopted. During such a process, the prepackaged foods in cans or pouches are put into a autoclave which is filled with the hot water or steam used as the medium of the thermal process. People can, under some particular requirements, have the appropriate control of the sterilization process by adjusting the temperature of the medium. After a planned time, the heat process is stopped and the hot water or steam is cooled, which finish the sterilization. In the whole procedure, the aim is twofold. One is, to the utmost extent, to destroy the microorganisms which cause the food spoilage, while the other one is to keep the nutrient ingredients of foods in sterilization as much as possible. The contradicting intents make the sterilization process control difficult to build a sensitive balance between them. If we keep the time long enough and the heating temperature high enough, the harmful bacterium can be fully killed but at the same time it also damages the nutrient ingredients largely. This is not a satisfying result that we want to attain. On the contrary, if we, in a short time, heat the food at the low temperature, the nutrient ingredients of foods will be well saved but the effect of sterilization is rebated. This also violates the original intention of the sterilization. To overcome these difficulties and get the ideal sterilization effect, not only the chemical and food engineers and agriculture engineers but also applied mathematicians try to find a really effective control strategy. It should be remarked that the first reference dealing with the problem from a mathematical point of view is Bermúdez & Martı́nez (1994), where the 3D control problem is stated, an optimality