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DCL Seminar: Rafal Goebel - Some Control Problems Where Convex and Set-Valued Analysis is Helpful

Event Type
Decision and Control Laboratory, Coordinated Science Laboratory
CSL Auditorium, Room B02
Sep 14, 2016   3:00 pm  
Rafal Goebel, Ph.D. Loyola University Chicago
Linda Meccoli

Decision and Control Lecture Series

Coordinated Science Laboratory


“Some Control Problems Where Convex and Set-Valued Analysis is Helpful”


Rafal Goebel, Ph.D.

Loyola University Chicago


Wednesday, September 14, 2016

3:00 p.m. to 4:00 p.m.

CSL Auditorium (B02)



“Some Control Problems Where Convex and Set-Valued Analysis is Helpful” 



Convex analysis, set-valued analysis, as well as nonsmooth analysis are subsumed by variational analysis, a modern branch of mathematical analysis which helps one deal with lack of differentiability, with multiple solutions to equations, with irregular dependence of solutions on parameters, etc. Convex analysis found early motivation in optimization and then greatly contributed to the field, for example by providing the convex duality framework for optimization problems. Nonmsooth analysis found early motivation in optimal control and contributed, for example, versions of the Pontryagin's Maximum Principle applicable to problems with constraints and irregular penalties.


Tools from convex and set-valued analysis are also applicable to various problems in control theory, not just in optimal control. The talk will present examples of this, some of which will come from recent research by the speaker. Passing to set-valued dynamics will be motivated by the effect of measurement error on control systems; convex, but not quadratic, Lyapunov functions will be used to justify duality between stability or between controllability and observability in uncertain or constrained linear systems; etc. No previous experience in variational analysis by the audience will be assumed, and the talk is meant more as an advertisement for variational analysis than as an in-depth treatment of any particular problem.


Rafal Goebel received his Ph.D. in mathematics in 2000 from the University of Washington. He held postdoctoral positions at the Departments of Mathematics at University of British Columbia and Simon Fraser University in Vancouver, and at the Electrical and Computer Engineering Department of University of California, Santa Barbara. In 2008, he joined the Department of Mathematics and Statistics at Loyola University Chicago. He received the 2009 SIAM Control and Systems Theory Prize and is a co-author of the Hybrid Dynamical Systems: Modeling, Stability, and Robustness book. His interests include convex, nonsmooth, and set-valued analysis; control, including optimal control; hybrid dynamical systems; mountains; and optimization.

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