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Optimal Complexity Reduction of Piecewise Affine Models Based on Hyperplane Arrangements

Author(s):

T. Geyer, F.D. Torrisi, M. Morari
Conference/Journal:

vol. AUT04-01
Abstract:

This paper presents an algorithm that, given a piecewise affine (PWA) model, derives an equivalent PWA model that is minimal in the number of regions. The algorithm is based on the cells of the hyperplane arrangement which are already given, when the PWA model is the result of the mode enumeration algorithm. In particular, the algorithm executes a branch and bound on the markings of the cells of the hyperplane arrangement assuring optimality. As we refrain from solving additional LPs, the algorithm is not only optimal but also computational feasible. The applicability of the algorithm can be extended to derive minimal PWA representations of general PWA models by first computing the hyperplane arrangement. Examples illustrate the algorithm and show its computational effectiveness.

Further Information
Year:

2004
Type of Publication:

(04)Technical Report
Supervisor:



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% Autogenerated BibTeX entry
@TechReport { GeyTor:2004:IFA_492,
    author={T. Geyer and F.D. Torrisi and M. Morari},
    title={{Optimal Complexity Reduction of Piecewise Affine Models
	  Based on Hyperplane Arrangements}},
    institution={},
    year={2004},
    number={},
    address={},
    month=feb,
    url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=492}
}
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