NDSU Applied Mathematics Seminar - Spring 2010
Loyola University Chicago
Department of Mathematics and Statistics


Time: Thursdays, 4:00PM-4:50PM  
BVM Hall - Room 1102 (6349 N. Kenmore Avenue, Chicago, IL 60626) [map]

Organizers: Marian Bocea and Rafal Goebel

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Thursday, February 11 - RAFAL GOEBEL (Loyola University Chicago) -  A (mildly biased) survey of mathematical models of hybrid systems (Part II)
Abstract: Classical approach to dynamical systems categorizes each dynamical system as a continuous-time dynamical system or a discrete-time dynamical system. For example, systems of planets that evolve under Newton's laws or biological systems where populations of species grow or decay exponentially are continuous-time systems and have solutions parameterized by time. Your savings account balance that increases every month, recursively-defined sequences, binary values in an algorithm, etc. are examples of discrete-time systems and have solutions parameterized by natural numbers that count the number of transitions. Broadly understood, hybrid dynamical systems are dynamical systems that exhibit features characteristic of continuous-time dynamical systems and features characteristic of discrete-time systems. Modeling of cyber-physical systems that combine analog and digital components; of mechanical systems with impacts, where velocities may change instantaneously; of biological systems with impulses; etc. motivate the interest in hybrid systems in control theory and control engineering literature. There, one can find piecewise affine systems, complementarity systems, differential or hybrid automata, dynamical systems on time scales, hybrid inclusions, impulsive differential equations, measure-driven differential equations, switched systems, etc., all of which have hybrid features.
The talk will present several of these modeling frameworks, discuss some concepts of solutions to the models, and relate selected frameworks to hybrid inclusions. Part II of this talk is fairly independent of Part I, and little background beyond differential equations will be necessary.

Friday, February 26 - AARON YIP (Purdue University) - Title TBA