微波加热中最优控制理论研究

项目名称： 微波加热中最优控制理论研究

项目编号： No.11261011

项目类型： 地区科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 韦维

作者单位： 贵州大学

项目金额： 50万元

中文摘要： 微波加热在化工、制药、食品、材料、采矿等领域都有广泛应用。但加热过程中的热失控和加热不均匀现象，成为了微波加热中一个难以解决和富于挑战的问题。 本课题研究微波加热的最优控制问题。从理论上探讨在避免热失控的情形下，如何构造性能指标及选择控制策略，实现均匀加热。受控系统是恰当初边值条件下Maxwell方程和非线性热传导方程构成的耦合系统。具体研究内容：1.耦合系统解及解的性质；2.Bang-bang控制问题；3.时谐系统的边界控制问题；4.可传导材料的加热控制问题。 对此耦合系统及其最优控制问题的研究，可以加深对电磁场强度与热传导率之间的关系的了解，可以丰富无穷维最优控制理论的内容，还可为微波加热控制系统的设计提供理论依据。同时项目的研究将对本土科研人才的培养、成长及其科研团队的建设取到积极的作用。

中文关键词： 微波加热；最优控制；Maxwell方程；非线性热传导方程；耦合系统

英文摘要： This proposal addresses optimal control problems arising from microwave heating processes. The main goal in this project is to design various methods by choosing suitable control variables for microwave heating such that the temperature will have desired distribution in the final stage. The underlying system consists of Maxwell's equations coupled with nonlinear heat equation subject to appropriate initial-boundary conditions. The major challenge is that the underlying system is a highly nonlinear coupled system is difficult to analyze. In this proposal we propose several optimal control problems which will lead to achieve the desired goal. Some initial analysis is also provided. Microwave heating has many important applications in various industries such as sterilization for frozen foods and medical equipment. In comparison of traditional sterilization processes, this method is quick and saves water and energy, which in turn has positive effect on environment. The new technique also provides a way for developing a sustainable economic growth. In addition, the research will enrich the scientific knowledge about the interaction between the electromagnetic field and the thermal conduction.

英文关键词： Microwave Heating;；Optimal Control；Maxwell Equation；Nonlinear Heat Equation；Coupled System