Hierarchical observer for strongly detectable systems via second order sliding mode

Francisco J. Bejarano; Leonid Fridman; Alexander Poznyak

doi:10.1109/CDC.2007.4434968

Hierarchical observer for strongly detectable systems via second order sliding mode

Francisco J. Bejarano, Leonid Fridman, Alexander Poznyak

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

12 Scopus citations

Abstract

Based on the concept of strong detectability, and its relation with the concept of invariant zeros, it is seen that the condition of strong detectability is a necessary and sufficient condition for the estimation of the state vector of a system with unknown inputs appearing explicitly in both places, the plant and the output of the system. We suggest a hierarchical scheme for the design of an observer whose trajectories converge to those of the original vector state. For the realization of such observer we take advantage of the properties of the second-order super-twisting sliding-mode algorithm, which is used as a substitute of a differentiator. We give a numerical example that illustrates the designing scheme proposed here.

Original language	English
Title of host publication	Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3709-3714
Number of pages	6
ISBN (Print)	1424414989, 9781424414987
DOIs	https://doi.org/10.1109/CDC.2007.4434968
State	Published - 2007
Externally published	Yes
Event	46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States Duration: 12 Dec 2007 → 14 Dec 2007

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	46th IEEE Conference on Decision and Control 2007, CDC
Country/Territory	United States
City	New Orleans, LA
Period	12/12/07 → 14/12/07

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10.1109/CDC.2007.4434968

Cite this

Bejarano, F. J., Fridman, L., & Poznyak, A. (2007). Hierarchical observer for strongly detectable systems via second order sliding mode. In Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC (pp. 3709-3714). Article 4434968 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2007.4434968

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title = "Hierarchical observer for strongly detectable systems via second order sliding mode",

abstract = "Based on the concept of strong detectability, and its relation with the concept of invariant zeros, it is seen that the condition of strong detectability is a necessary and sufficient condition for the estimation of the state vector of a system with unknown inputs appearing explicitly in both places, the plant and the output of the system. We suggest a hierarchical scheme for the design of an observer whose trajectories converge to those of the original vector state. For the realization of such observer we take advantage of the properties of the second-order super-twisting sliding-mode algorithm, which is used as a substitute of a differentiator. We give a numerical example that illustrates the designing scheme proposed here.",

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year = "2007",

doi = "10.1109/CDC.2007.4434968",

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isbn = "1424414989",

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note = "46th IEEE Conference on Decision and Control 2007, CDC ; Conference date: 12-12-2007 Through 14-12-2007",

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Bejarano, FJ, Fridman, L & Poznyak, A 2007, Hierarchical observer for strongly detectable systems via second order sliding mode. in Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC., 4434968, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 3709-3714, 46th IEEE Conference on Decision and Control 2007, CDC, New Orleans, LA, United States, 12/12/07. https://doi.org/10.1109/CDC.2007.4434968

Hierarchical observer for strongly detectable systems via second order sliding mode. / Bejarano, Francisco J.; Fridman, Leonid; Poznyak, Alexander.
Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. Institute of Electrical and Electronics Engineers Inc., 2007. p. 3709-3714 4434968 (Proceedings of the IEEE Conference on Decision and Control).

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

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AU - Fridman, Leonid

AU - Poznyak, Alexander

PY - 2007

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N2 - Based on the concept of strong detectability, and its relation with the concept of invariant zeros, it is seen that the condition of strong detectability is a necessary and sufficient condition for the estimation of the state vector of a system with unknown inputs appearing explicitly in both places, the plant and the output of the system. We suggest a hierarchical scheme for the design of an observer whose trajectories converge to those of the original vector state. For the realization of such observer we take advantage of the properties of the second-order super-twisting sliding-mode algorithm, which is used as a substitute of a differentiator. We give a numerical example that illustrates the designing scheme proposed here.

AB - Based on the concept of strong detectability, and its relation with the concept of invariant zeros, it is seen that the condition of strong detectability is a necessary and sufficient condition for the estimation of the state vector of a system with unknown inputs appearing explicitly in both places, the plant and the output of the system. We suggest a hierarchical scheme for the design of an observer whose trajectories converge to those of the original vector state. For the realization of such observer we take advantage of the properties of the second-order super-twisting sliding-mode algorithm, which is used as a substitute of a differentiator. We give a numerical example that illustrates the designing scheme proposed here.

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U2 - 10.1109/CDC.2007.4434968

DO - 10.1109/CDC.2007.4434968

M3 - Contribución a la conferencia

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SN - 1424414989

SN - 9781424414987

T3 - Proceedings of the IEEE Conference on Decision and Control

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BT - Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 46th IEEE Conference on Decision and Control 2007, CDC

Y2 - 12 December 2007 through 14 December 2007

ER -

Bejarano FJ, Fridman L, Poznyak A. Hierarchical observer for strongly detectable systems via second order sliding mode. In Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC. Institute of Electrical and Electronics Engineers Inc. 2007. p. 3709-3714. 4434968. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2007.4434968

Hierarchical observer for strongly detectable systems via second order sliding mode

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