Convex optimization methods for model reduction

Model reduction and convex optimization are prevalent in science and engineering applications. In this thesis, convex optimization solution techniques to three different model reduction problems are studied.Parameterized reduced order modeling is important for rapid design and optimization of systems containing parameter dependent reducible sub-circuits such as interconnects and RF inductors. The first part of the thesis presents a quasi-convex optimization approach to solve the parameterized model order reduction problem for linear time-invariant systems. Formulation of the model reduction problem as a quasi-convex program allows the flexibility to enforce constraints such as stability and passivity in both non-parameterized and parameterized cases. Numerical results including the parameterized reduced modeling of a large RF inductor are given to demonstrate the practical value of the proposed algorithm.A majority of nonlinear model reduction techniques can be regarded as a two step procedure as follows. First the state dimension is reduced through a projection, and then the vector field of the reduced state is approximated for improved computation efficiency. Neither of the above steps has been thoroughly studied. The second part of this thesis presents a solution to a particular problem in the second step above, namely, finding an upper bound of the system input/output error due to nonlinear vector field approximation. The system error upper bounding problem is formulated as an L2 gain upper bounding problem of some feedback interconnection, to which the small gain theorem can be applied. A numerical procedure based on integral quadratic constraint analysis and a theoretical statement based on L2 gain analysis are given to provide the solution to the error bounding problem. The numerical procedure is applied to analyze the vector field approximation quality of a transmission line with diodes.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2008

Author dc:creator

• Sou, Kin Cheong, 1979-

Advisor dc:contributor.advisor

• Luca Daniel and Alexandre Megretski.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/45872

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/45872