A Semidefinite Programming Approach for Control of Systems Along Trajectories
Farhood, Mazen Habib
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https://hdl.handle.net/2142/83839
Description
Title
A Semidefinite Programming Approach for Control of Systems Along Trajectories
Author(s)
Farhood, Mazen Habib
Issue Date
2005
Doctoral Committee Chair(s)
Dullerud, Geir E.
Department of Study
Mechanical Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Mechanical
Language
eng
Abstract
The second approach amounts to parametrizing the system equations about the trajectory, resulting in a nonstationary linear parameter-varying (NLPV) model, and then constructing an NLPV synthesis. Synthesis conditions are derived for NLPV systems using an operator theoretic framework with the ℓ 2-induced norm as the performance measure. These conditions are given in terms of structured operator inequalities. In general, evaluating the validity of these conditions is an infinite dimensional convex optimization problem; however, if the initial system is eventually periodic, they reduce to a finite dimensional semidefinite programming problem. Also, we give systematic approaches for the model reduction of stable as well as stabilizable NLPV models, along with means for evaluating the error resulting from the reduction process.
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