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Modelling, dynamics and control of spatially
distributed systems such as those described by partial differential equations
and dynamical systems on lattices.
The emphasis will be on linear, constructive and algebraic techniques.
The material in the course will be strongly motivated by physical examples.
Prototype problems from spatially distributed arrays of dynamical systems and
hydrodynamic stability will be used to illustrate the theory. |
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Instructor:
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Bassam Bamieh
, 2333 ENG II, x.4490,
bamieh@engineering.ucsb.edu
Office Hours: TBA
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Coordinates:
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MW, 9:00-10:50, 2243 ENG II
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Required Text:
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Instructor's notes will be provided |
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Supplementary Texts
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- An Introduction to Infinite-Dimensional Linear Systems Theory by
R. F. Curtain and H.J. Zwart, Springer-Verlag, 1995
- State-Space and frequency-domain methods in the control of
distributed parameter systems by
S. P. Banks, Peter Peregrinus Ltd., 1983
- Stability and Stabilization of Infinite Dimensional Systems with Applications by
Z.H. Luo, B.Z.Guo and O. Morgul, Springer-Verlag, 1999
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Web Page:
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GauchoSpace |
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Prerequisites:
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ME243A/B (ECE230A/B) and a solid background in
advanced linear algebra. Familiarity with functional analysis
and a certain amount of ``mathematical maturity''
is helpful. Students will be expected to make up any missing mathematical background
using provided references. |
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TOPICS:
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- Examples and motivation, connections and equivalences between
finite and infinite dimensional systems, Carleman and Lie-Koopman
linearizations
- Abstract evolution equations, regularity, well posedness and semi-groups
- Stability and spectral conditions
- Controllability/Observability, optimal control, norms, and sensitivities of infinite dimensional systems
- Approximation and numerical methods
- Symmetries, arrays and spatial invariance, transform methods
- Swarming, Flocking and large Multi-vehicle systems
- Hydrodynamic stability and transition to turbulence
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