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Spring'07: EE 8235
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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 becoming prevalent in modern 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, robustness and sensitivity of infinite dimensional systems. Pseudospectra. Optimal control. Architectural issues in distributed control design. Optimality of localized distributed controllers. 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. A solid background in linear systems and linear algebra is required. Some familiarity with functional analysis and a certain level of mathematical maturity is also helpful. Those interested should contact the instructor. |
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Class schedule:
TuTh 2:30pm - 3:45pm, Amundson Hall 120, January 16 - May 4 |
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| Instructor and TA
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| Texts/notes and software
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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 |
Erwin Kreyszig
Introductory functional analysis with applications
Wiley, First Edition, ISBN 0-471-50459-9 |
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Software |
Homework sets and class project will make a use of Matlab
and
Simulink
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| Suggested project list
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1. Infinite dimensional equivalents of nonlinear dynamical systems (Carleman and Lie-Koopman linearizations)
2. Boundary control of partial differential equations
3. Pseudospectra of linear operators
4. Hydrodynamic stability of different flow conditions
5. Flow control
6. Convective and absolute instabilities
7. Pattern formation in reaction-diffusion systems
8. Stability and robustness of bio-chemical reactions
9. Swarming, flocking, multi-vehicle coordination
10. Distributed optimization algorithms
11. Robustness of consensus algorithms
12. Distributed estimation
13. Distributed control
14. Parametric resonance in partial differential equations |
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This is just a partial list of potential
projects. Please feel free to suggest an alternative project you may be
interested in doing.
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