MULTIPLICATIVE NOISE AS A STRUCTURED STOCHASTIC UNCERTAINTY PROBLEM
Linear systems with multiplicative, time-varying noise exhibit varied and rich phenomenology such as heavy tails and dramatic differences between different notions of convergence. We study such systems in a framework similar to that used in robust control where the stochastic parameters are viewed as a "structured uncertainty". In particular, a purely input-output approach is developed to characterize mean-square stability. This approach clarifies earlier results in this area and also easily produces new ones in the case of correlated uncertainties. Applications of this framework to networked dynamical systems with link failures and stochastic topologies will be illustrated. In addition, an application to a model of the Cochlea will be described which potentially explains otoacoustic emissions as an instability mechanism. Finally, we illustrate some interesting connections of this work with the phenomenon of Anderson Localization which is a canonical problem in the statistical physics of disordered media.
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- Date: 27 Apr 2021
- Time: 07:00 PM to 08:00 PM
- All times are (UTC-04:00) Eastern Time (US & Canada)
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- Starts 01 March 2021 12:01 AM
- Ends 27 April 2021 03:00 PM
- All times are (UTC-04:00) Eastern Time (US & Canada)
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Speakers
Dr. Bassam Bamieh of MECHANICAL ENGINEERING DEPARTMENT, UNIVERSITY OF CALIFORNIA, SANTA BARBARA.
MULTIPLICATIVE NOISE AS A STRUCTURED STOCHASTIC UNCERTAINTY PROBLEM
Linear systems with multiplicative, time-varying noise exhibit varied and rich phenomenology such as heavy tails and dramatic differences between different notions of convergence. We study such systems in a framework similar to that used in robust control where the stochastic parameters are viewed as a "structured uncertainty". In particular, a purely input-output approach is developed to characterize mean-square stability. This approach clarifies earlier results in this area and also easily produces new ones in the case of correlated uncertainties. Applications of this framework to networked dynamical systems with link failures and stochastic topologies will be illustrated. In addition, an application to a model of the Cochlea will be described which potentially explains otoacoustic emissions as an instability mechanism. Finally, we illustrate some interesting connections of this work with the phenomenon of Anderson Localization which is a canonical problem in the statistical physics of disordered media.
Biography:
Dr. Bassam Bamieh is Professor of Mechanical Engineering at the University of California at Santa Barbara. He received his B.Sc. degree in Electrical Engineering and Physics from Valparaiso University (Valparaiso, IN) in 1983, and his M.Sc. and PhD degrees in Electrical and Computer Engineering from Rice University (Houston, TX) in 1986 and 1992 respectively. Prior to joining UCSB in 1998, he was an Assistant Professor in the Department of Electrical and Computer Engineering and the Coordinated Science Laboratory at the University of Illinois at Urbana-Champaign (1991-98). His current research interests include Robust and Optimal Control, distributed control and dynamical systems, shear flow transition and turbulence, and active control in thermoacoustic energy conversion devices. He received several awards and honors for his research, including an IEEE Control Systems Society G. S. Axelby Outstanding Paper Award, an AACC Hugo Schuck Best Paper Award, and a National Science Foundation CAREER award. He is a Distinguished Lecturer of the IEEE Control Systems Society, a Fellow of the International Federation of Automatic Control (IFAC), and a Fellow of the IEEE
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Address:California, United States, 93106