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Stochastic Sylvester equations for output regulation of linear stochastic systems

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Abstract: The characterization of the steady-state response of dynamical systems is at the basis of the solution of several problems in the control and systems field. In this talk, a characterization of the steady-state response of a general class of linear stochastic systems is considered. The steady-state response is characterized in terms of a stochastic differential matrix equation, which is a generalization of the Sylvester equation. This result is then applied to classical and recent problems in control systems, namely the output regulation problem and the model reduction problem. Unfortunately, but not surprisingly, the solution of the output regulation problem is not causal. By defining a new approximate problem and introducing hybrid control structures, the variations of the Brownian motion are estimated a posteriori. These estimates are then used to construct a causal approximation of the ideal solution.

Biography: Dr. Giordano Scarciotti is a Lecturer at Imperial College London. He received his B.Sc. and M.Sc. degree in Automation Engineering from the University of Rome Tor Vergata, Italy, in 2010 and 2012, respectively. In 2012 he joined the Control and Power Group, Imperial College London, where he obtained a Ph.D. degree in 2016 with a thesis on approximation, analysis and control of large-scale systems. His current research interests are focused on analysis and control of uncertain systems (modeled by stochastic equations), the problem of model reduction and problems of optimal control. He was a visiting scholar at New York University in 2015 and at University of California Santa Barbara in 2016. He is the recipient of a Junior Research Fellowship, now known as Imperial College Research Fellowship, of the IET Control & Automation PhD Award (2016), the Eryl Cadwaladr Davies Prize (2017) and an ItalyMadeMe award (2017).

This talk is part of the CUED Control Group Seminars series.

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