EE 8235: Fall 2011 Web Page
Mihailo Jovanovic, University of Minnesota

Modeling, Dynamics, and Control of Distributed Systems

Course description
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Course description:
This course deals with modeling, analysis, and
control of distributed dynamical systems. These systems are
typically described by partial differential equations (PDEs) or
interconnected systems of ordinary differential equations (ODEs),
and they are of increasing importance in modern science and
technology. The course content will be strongly motivated by
physical examples ranging from distributed networks of
interconnected systems to the problems from hydrodynamic stability
and transition to turbulence.

Topics:
Examples and motivation. Connections and equivalences
between finite and infinite dimensional systems. Abstract evolution
equations, regularity, well posedness and semigroups. Exponential
stability. Lyapunov functionals. Spectral conditions for stability.
Approximation and numerical methods. Symmetries, arrays and spatial
invariance. Transform methods. Spatiotemporal frequency responses.
Inputoutput norms, sensitivity, and robustness of infinite
dimensional systems. Pseudospectra. Optimal distributed control.
Architectural issues in distributed control design. Optimality of
localized distributed controllers. Distributed optimization.
Cardinality optimization problems. Alternating direction method of
multipliers. Consensus problem in sensor networks. Cooperative
control of largescale vehicle formations. Swarming and flocking.
Hydrodynamic stability and transition to turbulence. Pattern
formation in reactiondiffusion systems. Parametric resonance in
spatiotemporal systems. Spatiotemporal vibrational control.

Audience:
This course is aimed at attracting a spectrum of students
from across classical engineering disciplines, physics, and applied
mathematics. Even though I plan to cover everything from scratch, a
solid background in linear systems and linear algebra would be
helpful. Those interested should contact the instructor. 
Class schedule:
TuTh 9:45am  11:00am, MechE 108, Sept. 6  Dec. 14 

Instructor and TA
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Background material
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Linear Systems 1

Stephen Boyd
Introduction to Linear Dynamical Systems
Web page: Stanford
Notes
(videos, reader, slides, homework, …) 
Linear Systems 2

Stephen Boyd
Linear Dynamical Systems
Web page: Stanford
Notes
(slides, homework, …) 
Functional Analysis 
Erwin Kreyszig
Introductory Functional Analysis with Applications
Wiley, First Edition, ISBN 0471504599 

Texts/notes
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Primary text 
Instructor's notes 
Supplementary text 1 
Ruth F. Curtain,
Hans J. Zwart
An Introduction to InfiniteDimensional Linear Systems Theory
SpringerVerlag, First Edition, ISBN 0387944753 
Supplementary text 2

Stephen P. Banks
StateSpace and FrequencyDomain Methods
in the Control of Distributed Parameter Systems
Peter Peregrinus Ltd., First Edition, ISBN 0863410006 
Supplementary text 3

ZhengHua Luo, BaoZhu Guo, Omer Morgul
Stability and Stabilization of Infinite Dimensional Systems with Applications
SpringerVerlag, First Edition, ISBN 1852331240 
Supplementary text 4 
Mehran Mesbahi, Magnus Egerstedt
Graph Theoretic Methods in Multiagent Networks
Princeton University Press, First Edition, ISBN 9780691140612 

Software
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Matlab/Simulink 
Homework sets and class project will make use of Matlab
and
Simulink

Pseudospectral method for solving differential equations 
J. A. C. Weideman, Satish C. Reddy
A Matlab Differentiation Matrix Suite
Web page: Matlab Functions 
Chebfun 
Lloyd N. Trefethen and others
Chebfun Version 4
Web page: Chebfun V4.1.1864 
Pseudospectra Gateway 
Mark Embree, Lloyd N. Trefethen
Pseudospectra Gateway
Web page: Pseudospectra Gateway 
CVX: a package for specifying and solving convex programs 
Michael Grant, Stephen Boyd
CVX
Web page: CVX 

Course requirements
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Homework:
Homework is intended as a vehicle for learning, not as a test. I encourage you to collaborate with your classmates. Please try to invest enough time to understand each homework problem, and independently write the solutions that you turn in.
Exams:
We may have one take home exam in the second part of the semester.
Project:
A research project is a required portion of this course.
Each student will write a report and give a short project presentation at the end of
the semester. The project can either be an in depth study of a
relevant topic, or an original research idea (ideally something
related to your own research). I will suggest a list of potential
projects around the middle of the semester.

