Towards a Computationally Efficient Recursive Model Reduction and Controller Design Approach for Spatially Distributed Processes

本研究项目的目的是放宽基于数据的非线性降阶方法的要求，并扩展其在空间分布过程中出现的耗散偏微分方程（PDE）系统的控制和优化方面的适用性。为了实现这一目标，研究将首先专注于创建一种计算效率高的数据驱动算法，用于：a)推导耗散PDE系统的非线性低阶近似模型，专门用于控制和优化目的；b)表征低阶模型和PDE系统解决方案之间的误差。随后，研究将集中在实际可实现的反馈控制结构的综合，可以处理非线性、模型不确定性、约束和有限的测量可用性问题。同时，将解决空间分布进程的优化/最优操作策略的计算问题。这将通过推导一个系统方案来实现，该方案用于制定可适用于标准搜索算法的计算效率动态优化问题。研究成果将通过开发和传播具有透明用户-机器交互界面的软件转移到工业部门。分析、优化和严格控制传输反应过程将有利于广泛的工业关键工艺，如微电子和光伏制造的光刻反应器以及先进的催化反应器和工业玻璃炉。此外，将开展许多活动，将研究与教育结合起来，包括将研究成果纳入优化和控制课程，本科生通过荣誉课程参与研究，以及开发教育工具，如matlab附加组件，java applet和wiki。

The objective of this research project is to relax the requirements of data-based nonlinear order reduction methods and extend their applicability towards the control and optimization of dissipative partial differential equation (PDE) systems arising in the context of spatially distributed processes. To achieve this objective, the research will initially focus on creating a computationally efficient data-driven algorithm for: a) the derivation of nonlinear low-order, approximate models for dissipative PDE systems that are specifically tailored for control and optimization purposes, and b) characterization of the error between the low-order model and PDE system solutions. Subsequently, the research will focus on the synthesis of practically implementable feedback control structures that can deal with the issues of nonlinearity, model uncertainty, constrains and limited measurement availability. Concurrently, computational issues of optimization/optimal operation policies for spatially distributed processes will be resolved. This will be achieved via the derivation of a systematic scheme for the formulation of computationally efficient dynamic optimization problems that are amenable to standard search algorithms. The research results will be transferred into the industrial sector through the development and dissemination of software with a transparent user-machine interaction interface. Analyzing, optimizing and tightly controlling transport-reaction processes will benefit key processes of a wide range of industries such as lithographic reactors for microelectronics and photovoltaics fabrication and advanced catalytic reactors and industrial glass furnaces. Moreover, numerous activities will be pursued to integrate the research with education including incorporation of research results in optimization and control courses, undergraduate student participation in research through the honors program, and the development of educational tools such as matlab add-ons, java applets and wikis.