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Recent results on Sum of Squares-based systems analysis

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Abstract:
In this talk, I will present some recent results on Sum of Squares (SOS) methods in relation to dynamical systems analysis. I will first consider how to check the positivity of an integral inequality in one dimension, and how to apply this result to the problem of stability and input-output analysis of classes of Partial Differential Equations (PDEs) and delay differential equations using Lyapunov and dissipativity methods, giving a range of examples. I will also consider the problem of safety verification of systems described by PDEs via an extension to the notion of Barrier Certificates for ODEs to PDEs. This framework allows one to obtain functional output estimates for PDEs, which I will also discuss. Time permitting, I will talk about some promising directions for reducing the computational burden in Lyapunov analysis and how this can be applied to address the scalability questions that current SOS methods face.

Type of Seminar:
IfA Seminar
Speaker:
Prof. Antonis Papachristodoulou
Department of Engineering Science, University of Oxford
Date/Time:
Apr 02, 2015   14:15
Location:

ETZ E 8, Gloriastrasse 35
Contact Person:

Prof. Lygeros
No downloadable files available.
Biographical Sketch:
In 2000 I obtained an MA/MEng degree in Electrical and Information Sciences from the University of Cambridge, U.K. In 2005 I completed a PhD in Control and Dynamical Systems at the California Institute of Technology, with a PhD Minor in Aeronautics. I joined the Department of Engineering Science at the University of Oxford in January 2006, where I am now an Associate Professor in Engineering Science (Control Engineering), a Tutorial Fellow at Worcester College, Oxford and the Director of the EPSRC & BBSRC Centre for Doctoral Training in Synthetic Biology. In 2015 I was awarded the European Control Award for my contributions to robustness analysis and applications to networked control systems and systems biology. I serve regularly on Technical Programme Committees for conferences, and I am associate editor for Automatica and IEEE Transactions on Automatic Control.