Hybrid Dynamics and Control

 Rafal Goebel photo

Wednesdays@NICO Seminar, Noon, January 23 2013, Chambers Hall, Lower Level 

Prof. Rafal Goebel, Loyola University Chicago

Abstract

Hybrid dynamical systems feature variables which may change gradually and instantaneously, for example due to interaction of Newton's or circuit laws with impacts, switches, communication links, or algorithms involving logic. The talk will present several mathematical frameworks for modeling and analysis of such systems and then focus on hybrid inclusions, which combine differential inclusions, difference inclusions, and constraints.  Relevance of hybrid inclusions for modern control algorithms, which involve timers or switching and are often implemented with digital components, will be underlined. Elements of recently established robust asymptotic stability theory for hybrid inclusions will be presented.  


Biography

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.  His interests include convex, nonsmooth, and set-valued analysis; control, including optimal control; hybrid dynamical systems; mountains; and optimization. More information can be found here at Professor Goebel's website.