Large-Scale and Parallel Matrix Computations in Linear Control

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This interdisciplinary project will be devoted to the study of effective numerical methods for large-scale solutions and parallel computations of several fundamental linear algebra problems arising in the design and analysis of linear control systems. Specific attention will be paid to the development and implementation of computationally viable algorithms for: feedback stabilization of the large second-order model; computing the frequency response and the H-infinity norm of a large and sparse matrix; and parallel and high performance computing of important matrix equations such as the Lyapunov, Sylvester, and Riccati and the eigenvalue assignment problems. Some numerical analysis aspects such as conditioning of the problems and stability of the algorithms will be considered, as well. The use of state-of-the-art techniques in matrix computations such as the GMRES and QMR algorithms, Rank Revealing QR factorizations, condition estimations schemes such as SPICE, ICE, ACE, etc., and the associated software packages (e.g. LAPACK) will be emphasized. The algorithms to be developed in this project and their implementations on vector supercomputer and massive parallel architectures will permit fast, accurate, and reliable solutions of large-scale control problems arising in practical situations such as the design of large space structures, control of power systems, and for other problems that otherwise could not be handled in a reasonable time, if at all. The proposed research will thus address some of the critical needs for research in the area of large-scale and parallel computations in control theory outlined in the recent panel report "Future Directions in Control Theory: A Mathematical Perspective". The project is timely and benefit both applied mathematicians and control theorists and engineers.