ACAE Seminar

Title: Generalized LQR Control and Kalman Filtering with Relations to Computations of Inner-Outer and Spectral Factorizations
Speaker: Prof. Guoxiang Gu
Department of Electrical and Computer Engineering
Louisiana State University, USA
Date: Jan 17, 2006 Tuesday
Time: 4:00 p.m. - 5:00 p.m.
Venue: Room 215, William M. W. Mong Engineering Building, CUHK

Abstract
We investigate the generalized LQR control where the dimension of the control input is strictly greater than the dimension of the controlled output, and the weighting matrix on the control signal is singular. The dual problem is the generalized Kalman filtering where the dimension of the input noise process is strictly smaller than the dimension of the output measurement, and the covariance of the observation noise is singular. These two problems are intimately related to inner-outer factorizations for non-square stable transfer matrices with square inners of the smaller size. Such inner-outer factorizations are in turn related to spectral factorizations for power spectral density (PSD) matrices whose normal ranks are not full. We propose iterative algorithms and establish their convergence for spectral factorizations with applications to inner-outer factorizations, which in turn solve the generalized LQR control and Kalman filtering.

Biography
Guoxiang Gu received the B.S. degree in electrical engineering from Chinese Textile University, Shanghai, China in 1982, and the M.S. and Ph.D. degrees in electrical engineering from University of Minnesota, Minneapolis, in 1985 and 1988 respectively.
From 1988 to 1990, he was with the Department of Electrical Engineering, Wright State University, Dayton, OH, as a Visiting Assistant Professor. Since 1990, he joined Louisiana State University where he is currently a professor of electrical and computer engineering. His research interests include control, system identification, and digital signal processing. Dr. Gu has published over 50 archive journal papers and numerous book chapters and conference papers. He has held visiting positions in Wright-Patterson Airce Force Base and in Hong Kong University of Science and Technology. He served as an associate editor for IEEE Transactions on Automatic Control from 1999 to 2001 and now serves as an associate editor for SIAM Journal on Control and Optimization. He is presently the F.Hugh Coughlin/CLECO Distinguished Professor of Electrical Engineering at LSU.

***** ALL ARE WELCOME *****

Enquiries: Ms. Winnie Wong or Prof. Charlie Wang Chang-ling, Department of Automation and Computer-Aided Engineering, CUHK at 2609 8337. *ACAE Series (2005-06) is contained in the World-Wide Web home page at http://www.acae.cuhk.edu.hk/en/seminars/seminars.htm

Title:	Generalized LQR Control and Kalman Filtering with Relations to Computations of Inner-Outer and Spectral Factorizations
Speaker:	Prof. Guoxiang Gu Department of Electrical and Computer Engineering Louisiana State University, USA
Date:	Jan 17, 2006 Tuesday
Time:	4:00 p.m. - 5:00 p.m.
Venue:	Room 215, William M. W. Mong Engineering Building, CUHK
Abstract We investigate the generalized LQR control where the dimension of the control input is strictly greater than the dimension of the controlled output, and the weighting matrix on the control signal is singular. The dual problem is the generalized Kalman filtering where the dimension of the input noise process is strictly smaller than the dimension of the output measurement, and the covariance of the observation noise is singular. These two problems are intimately related to inner-outer factorizations for non-square stable transfer matrices with square inners of the smaller size. Such inner-outer factorizations are in turn related to spectral factorizations for power spectral density (PSD) matrices whose normal ranks are not full. We propose iterative algorithms and establish their convergence for spectral factorizations with applications to inner-outer factorizations, which in turn solve the generalized LQR control and Kalman filtering.
Biography Guoxiang Gu received the B.S. degree in electrical engineering from Chinese Textile University, Shanghai, China in 1982, and the M.S. and Ph.D. degrees in electrical engineering from University of Minnesota, Minneapolis, in 1985 and 1988 respectively. From 1988 to 1990, he was with the Department of Electrical Engineering, Wright State University, Dayton, OH, as a Visiting Assistant Professor. Since 1990, he joined Louisiana State University where he is currently a professor of electrical and computer engineering. His research interests include control, system identification, and digital signal processing. Dr. Gu has published over 50 archive journal papers and numerous book chapters and conference papers. He has held visiting positions in Wright-Patterson Airce Force Base and in Hong Kong University of Science and Technology. He served as an associate editor for IEEE Transactions on Automatic Control from 1999 to 2001 and now serves as an associate editor for SIAM Journal on Control and Optimization. He is presently the F.Hugh Coughlin/CLECO Distinguished Professor of Electrical Engineering at LSU.
*** ALL ARE WELCOME ***
Enquiries: Ms. Winnie Wong or Prof. Charlie Wang Chang-ling, Department of Automation and Computer-Aided Engineering, CUHK at 2609 8337. *ACAE Series (2005-06) is contained in the World-Wide Web home page at http://www.acae.cuhk.edu.hk/en/seminars/seminars.htm