State and Event Estimation of LTI Systems under Irregular and Random Sampling

Speaker: Le Yi Wang

Affiliation: Wayne State University, USA

Time: Tuesday 11/06/2013 from 11:00 to 12:00

Venue: Access Grid UWS. Presented from Penrith (Y239), accessible from Parramatta (EB.1.32) and Campbelltown (26.1.50).

Abstract: This presentation summarizes recent development on state and event estimation under irregular and random sampling schemes. The problem is primarily motivated by systems with limited sensor or network resources in which the sampling points are either triggered by sensor switching, or events, or certain PWM-based schemes, or randomly. State observability may be lost and the traditional observers may fail in general, even if the system has a full-rank observability matrix. We will show that if the original system is observable, the irregularly sampled system will be observable if the sampling density is higher than some critical frequency, independent of the actual sampling times. This result extends Shannon's sampling theorem for signal reconstruction under periodic sampling to system observability under arbitrary sampling sequences. State observers and recursive algorithms are developed whose convergence properties are derived under potentially dependent measurement noises. Persistent excitation conditions are validated by designing sampling time sequences. By generating suitable switching time sequences, the designed state observers are shown to be convergent in mean square, with probability one, and with exponential convergence rates. Schemes for generating desired sampling sequences are summarised. When the system switches its dynamics, it introduces a hybrid system. Joint estimation of states and events in linear regime-switching systems will be discussed under irregular sampling schemes. In general, joint observability can be lost even if each subsystem is observable; the number of sampling points which is sufficient for estimating a subsystem's state is not sufficient for joint observability; Joint observability and sampling complexity are established. Observer design and convergence analysis are conducted for systems under noisy observations. When the sampling scheme is random, probabilistic characterization of observability will be presented under various sampling schemes and two regime-switching processes: renewal processes and Markov chains. We will show that regime switching may help enhancement of observability in the sense that the state may become observable even if subsystems are unobservable.

Biography: Le Yi Wang received the Ph.D. degree in electrical engineering from McGill University, Montreal, Canada, in 1990. Since 1990, he has been with Wayne State University, Detroit, Michigan, where he is currently a Professor in the Department of Electrical and Computer Engineering. His research interests are in the areas of complexity and information, system identification, robust control, H-infinity optimization, time-varying systems, adaptive systems, hybrid and nonlinear systems, information processing and learning, as well as medical, automotive, communications, power systems, and computer applications of control methodologies. He was a keynote speaker in several international conferences. He serves on the IFAC Technical Committee on Modeling, Identification and Signal Processing. He was an Associate Editor of the IEEE Transactions on Automatic Control and several other journals, and currently is an Editor of the Journal of System Sciences and Complexity and an Associate Editor of Journal of Control Theory and Applications. He is a Fellow of IEEE.