EE Systems Seminar: Constrained system identification of reaction-diffusion equations: a bridge between control and inverse problems | Dr. Rami Katz (University of Trento)
סמינר זה יחשב כסמינר שמיעה לתלמידי תואר שני
(The talk will be given in English)
Speaker: Dr. Rami Katz University of Trento
011 hall, Electrical Engineering-Kitot Building
Monday, June 25th, 2023
15:00 - 16:00
Constrained system identification of reaction-diffusion equations: a bridge between control and inverse problems
Abstract
System identification uses mathematical methods to reconstruct models of systems from partial and noisy data. The identification of reaction-diffusion (RD) systems is a mathematically intricate and significant research domain within systems and control, and finds application across diverse fields, spanning from multi-agent systems to chemical reactors. Many identification algorithms necessitate an infinite number of measurements and often fail to yield explicit bounds on recovery errors, in the presence of noise. In this talk, I will consider the problem of recovering the first dominant modes and initial condition of an unknown one-dimensional RD system from a finite set of filtered (noisy) state measurements. We demonstrate that Prony’s method for spike deconvolution, commonly applied in super-resolution problems, is suitable for solving this identification task. Moreover, building on recent results on the error sensitivity of Prony’s method, we derive new explicit identification guarantees, by analyzing the first-order condition numbers with respect to the measurement filtering error and showing their (super) exponential decay to zero in several identification regimes. The developed tools establish a hitherto unexplored connection between systems and control theory and inverse problems.
Joint with D. Batenkov from the School of Mathematics at Tel Aviv University.
Short Bio
Rami Katz is a post-doctoral researcher at the University of Trento, Italy. Rami recieved his B.Sc. and M.Sc in applied mathematics and his Ph.D. in electrical engineering from Tel Aviv University. He is the recipient of the KLA and Weinstein fellowships, as well as several excellence awards for both studies and teaching. He is an ECC21 best student paper award finalist and the recipient of the June 2020 editor's choice in Automatica. His research interests include control of nonlinear and distributed parameter system, systems biology and inverse problems in signal processing and control.
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