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

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

doi:10.1109/TAC.2006.876952

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

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

Center for Analysis, Scientific Computing and Applications

Research output: Contribution to journal › Article › Academic › peer-review

211 Citations (Scopus)

6 Downloads (Pure)

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.

Original language	English
Pages (from-to)	938-948
Journal	IEEE Transactions on Automatic Control
Volume	51
Issue number	6
DOIs	https://doi.org/10.1109/TAC.2006.876952
Publication status	Published - 2006

Access to Document

10.1109/TAC.2006.876952

Cite this

@article{2715ebf82e7a4b0cba5951636ae7738f,

title = "Reachability and control synthesis for piecewise-affine hybrid systems on simplices",

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.",

author = "L.C.G.J.M. Habets and P.J. Collins and {Schuppen, van}, J.H.",

year = "2006",

doi = "10.1109/TAC.2006.876952",

language = "English",

volume = "51",

pages = "938--948",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

publisher = "Institute of Electrical and Electronics Engineers",

number = "6",

}

TY - JOUR

T1 - Reachability and control synthesis for piecewise-affine hybrid systems on simplices

AU - Habets, L.C.G.J.M.

AU - Collins, P.J.

AU - Schuppen, van, J.H.

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

U2 - 10.1109/TAC.2006.876952

DO - 10.1109/TAC.2006.876952

M3 - Article

VL - 51

SP - 938

EP - 948

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 6

ER -

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

Abstract

Access to Document

Fingerprint

Cite this