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An algebraic geometry approach to nonlinear parametric optimization in control

Author(s):

I.A. Fotiou, Ph. Rostalski, B. Sturmfels, M. Morari
Conference/Journal:

American Control Conference, Minneapolis, MN, pp. 3618-3623
Abstract:

We present a method for nonlinear parametric optimization based on algebraic geometry. The problem to be studied, which arises in optimal control, is to minimize a polynomial function with parameters subject to semialgebraic constraints. The method uses Groebner bases computation in conjunction with the eigenvalue method for solving systems of polynomial equations. In this way, certain companion matrices are constructed off-line. Then, given the parameter value, an on-line algorithm is used to efficiently obtain the optimizer of the original optimization problem in real time.

Year:

2006
Type of Publication:

(01)Article
Supervisor:



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% Autogenerated BibTeX entry
@InProceedings { FotEtal:2006:IFA_2224,
    author={I.A. Fotiou and Ph. Rostalski and B. Sturmfels and M. Morari},
    title={{An algebraic geometry approach to nonlinear parametric
	  optimization in control}},
    booktitle={American Control Conference},
    pages={3618--3623},
    year={2006},
    address={Minneapolis, MN},
    month=jun,
    url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=2224}
}
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