A topological obstruction to reach control by continuous state feedback

Melkior Ornik; Mireille E. Broucke

doi:10.1109/CDC.2015.7402543

A topological obstruction to reach control by continuous state feedback

Melkior Ornik, Mireille E. Broucke

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

The reach control problem (RCP) deals with finding a feedback control which drives the states of an affine control system to leave a simplex through a predetermined facet. In analogy with Brockett's obstruction to continuous feedback stabilization, a topological obstruction to solving the RCP by continuous feedback results in a deep necessary condition for solvability. In this paper, we interpret the problem of topological obstruction as a problem of existence of null-homotopic maps on spheres. This results in a complete and easily implementable characterization of the topological obstruction for the case of systems with two inputs.

Original language	English (US)
Title of host publication	54rd IEEE Conference on Decision and Control,CDC 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2258-2263
Number of pages	6
ISBN (Electronic)	9781479978861
DOIs	https://doi.org/10.1109/CDC.2015.7402543
State	Published - Feb 8 2015
Externally published	Yes
Event	54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan Duration: Dec 15 2015 → Dec 18 2015

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	54rd IEEE Conference on Decision and Control,CDC 2015
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	54th IEEE Conference on Decision and Control, CDC 2015
Country/Territory	Japan
City	Osaka
Period	12/15/15 → 12/18/15

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Online availability

10.1109/CDC.2015.7402543

Library availability

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Ornik, M., & Broucke, M. E. (2015). A topological obstruction to reach control by continuous state feedback. In 54rd IEEE Conference on Decision and Control,CDC 2015 (pp. 2258-2263). Article 7402543 (Proceedings of the IEEE Conference on Decision and Control; Vol. 54rd IEEE Conference on Decision and Control,CDC 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2015.7402543

A topological obstruction to reach control by continuous state feedback. / Ornik, Melkior; Broucke, Mireille E.
54rd IEEE Conference on Decision and Control,CDC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 2258-2263 7402543 (Proceedings of the IEEE Conference on Decision and Control; Vol. 54rd IEEE Conference on Decision and Control,CDC 2015).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Ornik, M & Broucke, ME 2015, A topological obstruction to reach control by continuous state feedback. in 54rd IEEE Conference on Decision and Control,CDC 2015., 7402543, Proceedings of the IEEE Conference on Decision and Control, vol. 54rd IEEE Conference on Decision and Control,CDC 2015, Institute of Electrical and Electronics Engineers Inc., pp. 2258-2263, 54th IEEE Conference on Decision and Control, CDC 2015, Osaka, Japan, 12/15/15. https://doi.org/10.1109/CDC.2015.7402543

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A topological obstruction to reach control by continuous state feedback

Abstract

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