Interval Estimation for Second-Order Delay Differential Equations with Delayed Measurements and Uncertainties

T. Kharkovskaia; D. Efimov; E. Fridman; A. Polyakov; J. P. Richard

doi:10.1109/CDC.2018.8619424

Interval Estimation for Second-Order Delay Differential Equations with Delayed Measurements and Uncertainties

T. Kharkovskaia, D. Efimov, E. Fridman, A. Polyakov, J. P. Richard

School of Electrical Engineering

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

Abstract

The interval estimation design is studied for a second-order delay differential equation with position delayed measurements, uncertain input and initial conditions. The proposed method contains two consecutive interval observers. The first one estimates the interval of admissible values for the position without delay for each instant of time using new delay-dependent conditions on positivity. Then derived interval estimates of the position are used to design the second observer estimating an interval of admissible values for the velocity of the considered dynamical system. The results are illustrated by numerical experiments for an example.

Original language	English
Title of host publication	2018 IEEE Conference on Decision and Control, CDC 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5457-5462
Number of pages	6
ISBN (Electronic)	9781538613955
DOIs	https://doi.org/10.1109/CDC.2018.8619424
State	Published - 2 Jul 2018
Event	57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: 17 Dec 2018 → 19 Dec 2018

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2018-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	57th IEEE Conference on Decision and Control, CDC 2018
Country/Territory	United States
City	Miami
Period	17/12/18 → 19/12/18

Funding

Funders	Funder number
Ministry of Education and Science of the Russian Federation
Israel Science Foundation	1128/14
Government Council on Grants, Russian Federation	08-08

Access to Document

10.1109/CDC.2018.8619424

Cite this

Kharkovskaia, T., Efimov, D., Fridman, E., Polyakov, A., & Richard, J. P. (2018). Interval Estimation for Second-Order Delay Differential Equations with Delayed Measurements and Uncertainties. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 5457-5462). Article 8619424 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8619424

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title = "Interval Estimation for Second-Order Delay Differential Equations with Delayed Measurements and Uncertainties",

abstract = "The interval estimation design is studied for a second-order delay differential equation with position delayed measurements, uncertain input and initial conditions. The proposed method contains two consecutive interval observers. The first one estimates the interval of admissible values for the position without delay for each instant of time using new delay-dependent conditions on positivity. Then derived interval estimates of the position are used to design the second observer estimating an interval of admissible values for the velocity of the considered dynamical system. The results are illustrated by numerical experiments for an example.",

author = "T. Kharkovskaia and D. Efimov and E. Fridman and A. Polyakov and Richard, {J. P.}",

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Kharkovskaia, T, Efimov, D, Fridman, E, Polyakov, A & Richard, JP 2018, Interval Estimation for Second-Order Delay Differential Equations with Delayed Measurements and Uncertainties. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619424, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 5457-5462, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 17/12/18. https://doi.org/10.1109/CDC.2018.8619424

Interval Estimation for Second-Order Delay Differential Equations with Delayed Measurements and Uncertainties. / Kharkovskaia, T.; Efimov, D.; Fridman, E. et al.
2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 5457-5462 8619424 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

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

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AB - The interval estimation design is studied for a second-order delay differential equation with position delayed measurements, uncertain input and initial conditions. The proposed method contains two consecutive interval observers. The first one estimates the interval of admissible values for the position without delay for each instant of time using new delay-dependent conditions on positivity. Then derived interval estimates of the position are used to design the second observer estimating an interval of admissible values for the velocity of the considered dynamical system. The results are illustrated by numerical experiments for an example.

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Kharkovskaia T, Efimov D, Fridman E, Polyakov A, Richard JP. Interval Estimation for Second-Order Delay Differential Equations with Delayed Measurements and Uncertainties. In 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc. 2018. p. 5457-5462. 8619424. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2018.8619424

Interval Estimation for Second-Order Delay Differential Equations with Delayed Measurements and Uncertainties

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