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EE 8235: Fall 2011 Web Page
Mihailo Jovanovic, University of Minnesota
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Modeling, Dynamics, and Control of Distributed Systems
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| 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.
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Topics:
Examples and motivation. Connections and equivalences
between finite and infinite dimensional systems. Abstract evolution
equations, regularity, well posedness and semi-groups. Exponential
stability. Lyapunov functionals. Spectral conditions for stability.
Approximation and numerical methods. Symmetries, arrays and spatial
invariance. Transform methods. Spatio-temporal frequency responses.
Input-output 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 large-scale vehicle formations. Swarming and flocking.
Hydrodynamic stability and transition to turbulence. Pattern
formation in reaction-diffusion systems. Parametric resonance in
spatio-temporal systems. Spatio-temporal vibrational control.
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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. |
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Class schedule:
TuTh 9:45am - 11:00am, MechE 108, Sept. 6 - Dec. 14 |
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| Instructor and TA
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| Background material
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Linear Systems 1
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Stephen Boyd
Introduction to Linear Dynamical Systems
Web page: Stanford
Notes
(videos, reader, slides, homework, …) |
Linear Systems 2
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Stephen Boyd
Linear Dynamical Systems
Web page: Stanford
Notes
(slides, homework, …) |
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Functional Analysis |
Erwin Kreyszig
Introductory Functional Analysis with Applications
Wiley, First Edition, ISBN 0-471-50459-9 |
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| Texts/notes
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Primary text |
Instructor's notes |
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Supplementary text 1 |
Ruth F. Curtain,
Hans J. Zwart
An Introduction to Infinite-Dimensional Linear Systems Theory
Springer-Verlag, First Edition, ISBN 0-387-94475-3 |
Supplementary text 2
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Stephen P. Banks
State-Space and Frequency-Domain Methods
in the Control of Distributed Parameter Systems
Peter Peregrinus Ltd., First Edition, ISBN 0-863-41000-6 |
Supplementary text 3
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Zheng-Hua Luo, Bao-Zhu Guo, Omer Morgul
Stability and Stabilization of Infinite Dimensional Systems with Applications
Springer-Verlag, First Edition, ISBN 1-852-33124-0 |
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Supplementary text 4 |
Mehran Mesbahi, Magnus Egerstedt
Graph Theoretic Methods in Multiagent Networks
Princeton University Press, First Edition, ISBN 9780691140612 |
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| Software
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Matlab/Simulink |
Homework sets and class project will make use of Matlab
and
Simulink
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Pseudospectral method for solving differential equations |
J. A. C. Weideman, Satish C. Reddy
A Matlab Differentiation Matrix Suite
Web page: Matlab Functions |
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Chebfun |
Lloyd N. Trefethen and others
Chebfun Version 4
Web page: Chebfun V4.1.1864 |
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Pseudospectra Gateway |
Mark Embree, Lloyd N. Trefethen
Pseudospectra Gateway
Web page: Pseudospectra Gateway |
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CVX: a package for specifying and solving convex programs |
Michael Grant, Stephen Boyd
CVX
Web page: CVX |
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| 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.
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