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Parametric Optimization and Optimal Control using Algebraic Geometry Methods

Author(s):

I.A. Fotiou, Ph. Rostalski, P.A. Parrilo, M. Morari
Conference/Journal:

International Journal of Control, vol. 79, no. 11, pp. 1340-1358
Abstract:

We present two algebraic methods to solve the parametric optimization problem that arises in nonlinear model predictive control. We consider constrained discrete-time polynomial systems and the corresponding constrained finite-time optimal control problem. The first method is based on cylindrical algebraic decomposition. The second uses Groebner bases and the eigenvalue method for solving systems of polynomial equations. Both methods aim at moving most of the computational burden associated with the optimization problem off-line, by pre-computing certain algebraic objects. Then, an on-line algorithm uses this pre-computed information to obtain the solution of the original optimization problem in real time. Introductory material is provided as appropriate and the algorithms are accompanied by illustrative examples.

Year:

2006
Type of Publication:

(01)Article
Supervisor:



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% Autogenerated BibTeX entry
@Article { FotEtal:2006:IFA_2387,
    author={I.A. Fotiou and Ph. Rostalski and P.A. Parrilo and M. Morari},
    title={{Parametric Optimization and Optimal Control using Algebraic
	  Geometry Methods}},
    journal={International Journal of Control},
    year={2006},
    volume={79},
    number={11},
    pages={1340--1358},
    month=nov,
    url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=2387}
}
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