A Nonlinear Optimal Control Problem Arising from a Sterilization Process for Packaged Foods

In this paper we study an optimization problem arising from a sterilization process for packaged foods by using a microwave heating method. The goal of the optimal control is to find the optimal frequency function such that the temperature profile at the final stage has a relative uniform distributi...

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Bibliographic Details
Published inApplied mathematics & optimization Vol. 77; no. 3; pp. 499 - 513
Main Authors Yin, Hong-Ming, Wei, Wei
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2018
Springer Nature B.V
Subjects
Calculus of Variations and Optimal Control; Optimization
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Control
FOOD
MAGNETIC FIELDS
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
MICROWAVE RADIATION
Nonlinear control
NONLINEAR PROBLEMS
Numerical and Computational Physics
OPTIMAL CONTROL
OPTIMIZATION
Simulation
STERILIZATION
Systems Theory
Theoretical
Optimal control for microwave sterilization
Optimal frequency
Time-harmonic Maxwell’s equations
35J70
35Q60
35K55
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Summary:In this paper we study an optimization problem arising from a sterilization process for packaged foods by using a microwave heating method. The goal of the optimal control is to find the optimal frequency function such that the temperature profile at the final stage has a relative uniform distribution in the food product. The underlying state variables are electric, magnetic fields and temperature which satisfy the coupled nonlinear Maxwell’s system and a nonlinear heat equation. The control variable for the system is chosen to be the electric frequency function. We show that there exists an optimal frequency which minimizes the cost functional. Moreover, an optimality condition is also derived.
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-016-9382-0