Suboptimal control of singularly perturbed systems and periodic optimization

Vladimir Gaitsgory

doi:10.1109/CDC.1992.371249

Suboptimal control of singularly perturbed systems and periodic optimization

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

Abstract

A traditional approach to singularly perturbed optimal control problems is based on an approximation of these problems by some reduced problems. The reduced problems are obtained via the formal replacement of the fast variables by the states of equilibrium of the fast subsystems considered with frozen slow variables and controls. It is shown that such as approximation may not be valid, and that it is valid if and only if certain families of periodic optimization problems admit steady-state solutions. It is also shown how the solutions of these problems can be used to construct suboptimal controls for singularly perturbed problems when the approximation by the reduced problems is not possible.

Original language	English
Title of host publication	Proceedings of the 31st IEEE conference on decision and control
Place of Publication	Piscataway, NJ
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	3044-3049
Number of pages	6
ISBN (Print)	0780308727
DOIs	https://doi.org/10.1109/CDC.1992.371249
Publication status	Published - 1992
Externally published	Yes
Event	31ST IEEE CONF ON DECISION AND CONTROL - Tucson, United States Duration: 16 Dec 1992 → 18 Dec 1992

Conference

Conference	31ST IEEE CONF ON DECISION AND CONTROL
Country/Territory	United States
City	Tucson
Period	16/12/92 → 18/12/92

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10.1109/CDC.1992.371249

Cite this

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title = "Suboptimal control of singularly perturbed systems and periodic optimization",

abstract = "A traditional approach to singularly perturbed optimal control problems is based on an approximation of these problems by some reduced problems. The reduced problems are obtained via the formal replacement of the fast variables by the states of equilibrium of the fast subsystems considered with frozen slow variables and controls. It is shown that such as approximation may not be valid, and that it is valid if and only if certain families of periodic optimization problems admit steady-state solutions. It is also shown how the solutions of these problems can be used to construct suboptimal controls for singularly perturbed problems when the approximation by the reduced problems is not possible.",

author = "Vladimir Gaitsgory",

year = "1992",

doi = "10.1109/CDC.1992.371249",

language = "English",

isbn = "0780308727",

pages = "3044--3049",

booktitle = "Proceedings of the 31st IEEE conference on decision and control",

publisher = "Institute of Electrical and Electronics Engineers (IEEE)",

address = "United States",

note = "31ST IEEE CONF ON DECISION AND CONTROL ; Conference date: 16-12-1992 Through 18-12-1992",

}

Gaitsgory, V 1992, Suboptimal control of singularly perturbed systems and periodic optimization. in Proceedings of the 31st IEEE conference on decision and control., FM2, Institute of Electrical and Electronics Engineers (IEEE), Piscataway, NJ, pp. 3044-3049, 31ST IEEE CONF ON DECISION AND CONTROL, Tucson, Arizona, United States, 16/12/92. https://doi.org/10.1109/CDC.1992.371249

Suboptimal control of singularly perturbed systems and periodic optimization. / Gaitsgory, Vladimir.
Proceedings of the 31st IEEE conference on decision and control. Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE), 1992. p. 3044-3049 FM2.

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

TY - GEN

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AU - Gaitsgory, Vladimir

PY - 1992

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N2 - A traditional approach to singularly perturbed optimal control problems is based on an approximation of these problems by some reduced problems. The reduced problems are obtained via the formal replacement of the fast variables by the states of equilibrium of the fast subsystems considered with frozen slow variables and controls. It is shown that such as approximation may not be valid, and that it is valid if and only if certain families of periodic optimization problems admit steady-state solutions. It is also shown how the solutions of these problems can be used to construct suboptimal controls for singularly perturbed problems when the approximation by the reduced problems is not possible.

AB - A traditional approach to singularly perturbed optimal control problems is based on an approximation of these problems by some reduced problems. The reduced problems are obtained via the formal replacement of the fast variables by the states of equilibrium of the fast subsystems considered with frozen slow variables and controls. It is shown that such as approximation may not be valid, and that it is valid if and only if certain families of periodic optimization problems admit steady-state solutions. It is also shown how the solutions of these problems can be used to construct suboptimal controls for singularly perturbed problems when the approximation by the reduced problems is not possible.

U2 - 10.1109/CDC.1992.371249

DO - 10.1109/CDC.1992.371249

M3 - Conference proceeding contribution

SN - 0780308727

SP - 3044

EP - 3049

BT - Proceedings of the 31st IEEE conference on decision and control

PB - Institute of Electrical and Electronics Engineers (IEEE)

CY - Piscataway, NJ

T2 - 31ST IEEE CONF ON DECISION AND CONTROL

Y2 - 16 December 1992 through 18 December 1992

ER -

Suboptimal control of singularly perturbed systems and periodic optimization

Abstract

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