Averaging of three time scale singularly perturbed control systems

Vladimir Gaitsgory; Minh Tuan Nguyen

doi:10.1016/S0167-6911(00)00111-0

Averaging of three time scale singularly perturbed control systems

Vladimir Gaitsgory^*, Minh Tuan Nguyen

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

We investigate the asymptotic properties of singularly perturbed control systems with three time scales. We apply the averaging method to construct a limiting system for the slowest motion in the form of a differential inclusion. Sufficient conditions for the uniform convergence of the slowest trajectories are given.

Original language	English
Pages (from-to)	395-403
Number of pages	9
Journal	Systems and Control Letters
Volume	42
Issue number	5
DOIs	https://doi.org/10.1016/S0167-6911(00)00111-0
Publication status	Published - 2001
Externally published	Yes

Keywords

Averaging method
Convex analysis
Differential inclusion
Hausdorff metric
Multi-time scales
Nonlinear control systems
Singular perturbation

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10.1016/S0167-6911(00)00111-0

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title = "Averaging of three time scale singularly perturbed control systems",

abstract = "We investigate the asymptotic properties of singularly perturbed control systems with three time scales. We apply the averaging method to construct a limiting system for the slowest motion in the form of a differential inclusion. Sufficient conditions for the uniform convergence of the slowest trajectories are given.",

keywords = "Averaging method, Convex analysis, Differential inclusion, Hausdorff metric, Multi-time scales, Nonlinear control systems, Singular perturbation",

author = "Vladimir Gaitsgory and Nguyen, {Minh Tuan}",

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doi = "10.1016/S0167-6911(00)00111-0",

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T1 - Averaging of three time scale singularly perturbed control systems

AU - Gaitsgory, Vladimir

AU - Nguyen, Minh Tuan

PY - 2001

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N2 - We investigate the asymptotic properties of singularly perturbed control systems with three time scales. We apply the averaging method to construct a limiting system for the slowest motion in the form of a differential inclusion. Sufficient conditions for the uniform convergence of the slowest trajectories are given.

AB - We investigate the asymptotic properties of singularly perturbed control systems with three time scales. We apply the averaging method to construct a limiting system for the slowest motion in the form of a differential inclusion. Sufficient conditions for the uniform convergence of the slowest trajectories are given.

KW - Averaging method

KW - Convex analysis

KW - Differential inclusion

KW - Hausdorff metric

KW - Multi-time scales

KW - Nonlinear control systems

KW - Singular perturbation

UR - http://www.scopus.com/inward/record.url?scp=0034922978&partnerID=8YFLogxK

U2 - 10.1016/S0167-6911(00)00111-0

DO - 10.1016/S0167-6911(00)00111-0

M3 - Article

AN - SCOPUS:0034922978

SN - 0167-6911

VL - 42

SP - 395

EP - 403

JO - Systems and Control Letters

JF - Systems and Control Letters

IS - 5

ER -

Averaging of three time scale singularly perturbed control systems

Abstract

Keywords

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