Applied Mathematics & Optimization

, Volume 77, Issue 3, pp 499–513

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

• Hong-Ming Yin
• Wei Wei
Article

## Abstract

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.

## Keywords

Time-harmonic Maxwell’s equations Optimal control for microwave sterilization Optimal frequency

## Mathematics Subject Classification

35Q60 35J70 35K55

## Notes

### Acknowledgments

Many thanks to the anonymous referees for their comments and suggestions. The main result of this paper was reported by the first author at SIAM Conference on Control and its Applications from July 8-10, 2015, at Paris, France. The work of the second author is supported by a Chinese Natural Science Research Grant No. 11261011.

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