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

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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.