Note: This content is accessible to all versions of every browser. However, this browser does not seem to support current Web standards, preventing the display of our site's design details.

  

Every Continuous Piecewise Affine Function Can Be Obtained by Solving a Parametric Linear Program

Author(s):

A.B. Hempel, P.J. Goulart, J. Lygeros
Conference/Journal:

European Control Conference (ECC), Zurich, Switzerland, pp. 2657-2662
Abstract:

It is well-known that solutions to parametric linear or quadratic programs are continuous piecewise affine functions of the parameter. In this paper we prove the converse, i.e. that every continuous piecewise affine function can be identified with the solution to a parametric linear program. In particular, we provide a constructive proof that every piecewise affine function can be expressed as the linear mapping of the solution to a parametric linear program with at most twice as many variables as the dimension of the domain of the piecewise affine function. Our method is illustrated via two small numerical examples.

Year:

2013
Type of Publication:

(01)Article
Supervisor:



File Download:

Request a copy of this publication.
(Uses JavaScript)
% Autogenerated BibTeX entry
@InProceedings { HemGou:2013:IFA_4223,
    author={A.B. Hempel and P.J. Goulart and J. Lygeros},
    title={{Every Continuous Piecewise Affine Function Can Be Obtained
	  by Solving a Parametric Linear Program}},
    booktitle={European Control Conference (ECC)},
    pages={2657--2662},
    year={2013},
    address={Zurich, Switzerland},
    month=jul,
    url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=4223}
}
Permanent link