Control to facet problems for affine systems on simplices and polytopes, with applications to control of hybrid systems

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

doi:10.1109/CDC.2005.1582817

Control to facet problems for affine systems on simplices and polytopes, with applications to control of hybrid systems

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

Center for Analysis, Scientific Computing and Applications

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

19 Citations (Scopus)

2 Downloads (Pure)

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.

Original language	English
Title of host publication	Proceedings 44th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC'05, Sevilla, Spain, December 12-15, 2005
Publisher	Institute of Electrical and Electronics Engineers
Pages	4175-4180
ISBN (Print)	0-7803-9568-9
DOIs	https://doi.org/10.1109/CDC.2005.1582817
Publication status	Published - 2005

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Habets, L. C. G. J. M., & Schuppen, van, J. H. (2005). Control to facet problems for affine systems on simplices and polytopes, with applications to control of hybrid systems. In Proceedings 44th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC'05, Sevilla, Spain, December 12-15, 2005 (pp. 4175-4180). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC.2005.1582817

Habets, L.C.G.J.M. ; Schuppen, van, J.H. / Control to facet problems for affine systems on simplices and polytopes, with applications to control of hybrid systems. Proceedings 44th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC'05, Sevilla, Spain, December 12-15, 2005. Institute of Electrical and Electronics Engineers, 2005. pp. 4175-4180

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title = "Control to facet problems for affine systems on simplices and polytopes, with applications to control of hybrid systems",

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.",

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

year = "2005",

doi = "10.1109/CDC.2005.1582817",

language = "English",

isbn = "0-7803-9568-9",

pages = "4175--4180",

booktitle = "Proceedings 44th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC'05, Sevilla, Spain, December 12-15, 2005",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

}

Habets, LCGJM & Schuppen, van, JH 2005, Control to facet problems for affine systems on simplices and polytopes, with applications to control of hybrid systems. in Proceedings 44th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC'05, Sevilla, Spain, December 12-15, 2005. Institute of Electrical and Electronics Engineers, pp. 4175-4180. https://doi.org/10.1109/CDC.2005.1582817

Control to facet problems for affine systems on simplices and polytopes, with applications to control of hybrid systems. / Habets, L.C.G.J.M.; Schuppen, van, J.H.
Proceedings 44th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC'05, Sevilla, Spain, December 12-15, 2005. Institute of Electrical and Electronics Engineers, 2005. p. 4175-4180.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AU - Schuppen, van, J.H.

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N2 - 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.

AB - 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.

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DO - 10.1109/CDC.2005.1582817

M3 - Conference contribution

SN - 0-7803-9568-9

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EP - 4180

BT - Proceedings 44th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC'05, Sevilla, Spain, December 12-15, 2005

PB - Institute of Electrical and Electronics Engineers

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Habets LCGJM, Schuppen, van JH. Control to facet problems for affine systems on simplices and polytopes, with applications to control of hybrid systems. In Proceedings 44th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC'05, Sevilla, Spain, December 12-15, 2005. Institute of Electrical and Electronics Engineers. 2005. p. 4175-4180 doi: 10.1109/CDC.2005.1582817

Control to facet problems for affine systems on simplices and polytopes, with applications to control of hybrid systems

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