NDSU Applied Mathematics Seminar - Spring 2010
**Loyola University Chicago **

Department of Mathematics and Statistics

ANALYSIS SEMINAR
**Time: Thursdays, 4:00PM-4:50PM**** **

Location: **BVM Hall - Room 1102****
(6349 N. Kenmore Avenue, Chicago, IL 60626)** [map]

**SPRING 2016
SCHEDULE**

**FEBRUARY 2016**
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**** **

Abstract:* *TBA