Control of Nonlinear Distributed Systems with Free Bounaries

本研究的目的是为具有自由边界的非线性分布系统的反馈控制发展适用的数学理论。主要的工作集中在通过耦合的纳维-斯托克斯方程和热方程来描述的系统上。这个问题的动机是精密反馈控制的晶体生长过程，以实现高质量的晶体和高生产率的发展。这个问题在微电子和光电子器件的制造中具有重要的基础意义。将进行计算机模拟研究，以确定所建议的反馈控制的有效性和可行性。利用神经网络对晶体生长过程进行建模和实时控制也将通过计算机模拟来探索，计算机模拟使用计算机生成的和真实的实验数据。

The objective of this proposed study is to develop applicable mathematical theories for the feedback control of nonlinear distributed systems with free-boundaries. The main effort is focused on systems describable by coupled Navier-Stokes and heat equations. This problem is motivated from the development of precision feedback controls for the crystal growth process to achieve high quality crystals and high productivity. This problem is of basic importance in the manufacturing of microelectronic and optoelectronic devices. Computer simulation studies will be made for determining effectiveness and feasibility of the proposed feedback controls. The use of neural networks for modelling and real-time control of the crystal growth process will also be explored by means of computer simulation using both computer generated and real experimental data.