|28. Juni 2016
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Prof. Bahman Gharesifard
Control Group Department of Mathematics and Statistics
Tuesday 2016-06-28 16:00
IST-Seminar-Room V9.22 - Pfaffenwaldring 9 - Campus Stuttgart-Vaihingen
In the first part of this talk, we study the asymptotic convergence properties of the saddle-point dynamics associated to continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We identify a suite of complementary conditions under which the set of saddle points is asymptotically stable under the saddle-point dynamics.
In the second part of the talk, we demonstrate the implications of these convergence result in designing continuous-time distributed convex optimization algorithm. We also demonstrate how such continuous-time dynamical systems can be formulated as the trajectories of a distributed control systems, where the control input to the dynamics of each agent relies on an observer that estimates the average state. Using this observation, and by incorporating a continuous-time version of the so-called push-sum algorithm, we relax the graph theoretic conditions under which the first component of the trajectories of this modified class of saddle-point dynamical systems for distributed optimization are asymptotically convergent to the set of optimizers. In particular, we prove that strong connectivity is sufficient under this modified dynamics, relaxing the commonly used weight-balanced assumption. As a by product, we also show that the saddle-point distributed optimization dynamics can be extended to time-varying weight-balanced graphs which satisfy a persistency condition on the min-cut of the sequence of Laplacian matrices.
Bahman Gharesifard is an Assistant Professor with the Department of Mathematics and Statistics, Queen's University, Canada. Prior to joining Queen's, he was a Postdoctoral Research Associate with the Coordinated Science Laboratory (CSL) at the University of Illinois, Urbana-Champaign (2012-2013) and Postdoctoral Researcher at the Cymer Center for Controls and Dynamics at the University of California in San Diego (2009-2012). He received a PhD degree in Mathematics from Queen's University, Canada, in 2009. His research interests include systems and controls, distributed optimization, social and economic networks, game theory, geometric control and mechanics, and Riemannian geometry.