Control to facet problems for affine systems on simplices and polytopes - With applications to control of hybrid systems

Author

Habets, L.C.G.J.M. ; van Schuppen, J.H.

Author_Institution

Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, NL -5600 MB Eindhoven, The Netherlands, and CWI - Centrum voor Wiskunde en Informatica, P.O. Box 94079, NL -1090 GB Amsterdam, The Netherlands. E-mail: l.c.g.

fYear

2005

fDate

15-15 Dec. 2005

Firstpage

4175

Lastpage

4180

Abstract

In this paper, a general control-to-facet problem for affine systems on polytopes is studied: find an affine feedback law such that all trajectories of the closed-loop system leave the state polytope through an a priori specified (possibly empty) set of facets. Solutions are presented in terms of (bi)linear inequalities in the coefficients of the affine feedback. The result is applied to control synthesis for piecewise-affine hybrid systems. Using a backward recursion algorithm, a sufficient condition for reachability of hybrid systems is obtained, and a piecewise-affine controller is computed that realizes the required reachability property.

Keywords

Automata; Automatic control; Control system synthesis; Control systems; Engines; Manifolds; Physics computing; State feedback; Sufficient conditions; Systems engineering and theory;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on

Conference_Location

Seville, Spain

Print_ISBN

0-7803-9567-0

Type

conf

DOI

10.1109/CDC.2005.1582817

Filename

1582817