Reachability and control synthesis for piecewise-affine hybrid systems on simplices

Author

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

Author_Institution

Dept. of Math. & Comput. Sci., Technische Univ. Eindhoven, Netherlands

Volume

51

Issue

6

fYear

2006

fDate

6/1/2006 12:00:00 AM

Firstpage

938

Lastpage

948

Abstract

In this paper, we consider the synthesis of control laws for piecewise-affine hybrid systems on simplices. The construction is based on the solution to the control-to-facet problem at the continuous level, and on dynamic programming at the discrete level. The construction is given as an explicit algorithm using only linear algebra and reach-set computations for automata; no numerical integration is required. The method is conservative, in that it may fail to find a control law where one exists, but one cannot hope for a sharp algorithm for control synthesis since reachability for piecewise-affine hybrid systems is undecidable.

Keywords

continuous time systems; control system synthesis; discrete systems; dynamic programming; linear algebra; piecewise constant techniques; reachability analysis; control synthesis; dynamic programming; linear algebra; piecewise-affine hybrid systems; reach-set computations; reachability; simplices; Automata; Automatic control; Control system synthesis; Control systems; Physics computing; Power engineering and energy; Power engineering computing; Robust stability; Safety; Systems engineering and theory; Discrete-event system (DES); exit facet; piecewise-affine hybrid systems; reachability; simplex; stability;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2006.876952

Filename

1643366