Computational Methods for Feedback Control Problems of Matrix Second Order and Distributed Parameter Systems

该项目将为分布参数系统和矩阵二阶微分方程系统建模的控制系统的反馈设计开发数值上可行的实用算法和相关理论。具体要考虑的问题有：部分特征值和特征结构分配、鲁棒特征结构分配、模型更新和最优控制。这种反馈问题出现在各种工业环境中，包括汽车、飞机、高层建筑、大空间结构以及电力和制造系统的设计。将特别注意在分布参数系统中解决它们自己的自然公式中的问题。直接处理此类系统的数值方法很少，然而，从实际应用的角度来看，直接解决问题而不离散到二阶系统是可取的；只有这样，才有可能避免丢失重要的内在信息。该项目的成果预计将影响多个行业，从汽车到计算机行业，再到航空航天和制造业应用；它们也将是计算机辅助控制系统设计和控制教育领域的宝贵工具。

This project will develop numerically viable practical algorithms and associated theories for feedback design of control systems modeled by distributed parameter systems and systems of matrix second-order differential equations. The specific problems to be considered are partial eigenvalue and eigenstructure assignments, robust eigenstructure assignment, model updating and optimal control. Such feedback problems arise in a variety of industrial contexts, including design of automobiles, aircraft, high-rise buildings, large-space structures, and power and manufacturing systems. Special attention will be given to solving the problems in their own natural formulations in distributed parameter systems. Numerical methods that deal directly with such systems are rare, yet, it is desirable, from practical application point-of-view, that the problems be solved directly without discretization to second-order systems; only by doing so, is it possible to avoid losing vital inherent information.The results of the project are expected to impact a variety of industries, from automotive to computer industries to aerospace and manufacturing applications; they will also be invaluable tools in the area of computer aided control systems design and control education.