Nonlinear averaging theorems, and the determination of parameter convergence rates in adaptive control

Marc Bodson; Shankar Sastry; Brian D.O. Anderson; Iven Mareels; Robert R. Bitmead

doi:10.1016/0167-6911(86)90108-8

Nonlinear averaging theorems, and the determination of parameter convergence rates in adaptive control

Marc Bodson^*, Shankar Sastry, Brian D.O. Anderson, Iven Mareels, Robert R. Bitmead

^*Corresponding author for this work

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

12 Citations (Scopus)

Abstract

The paper presents nonlinear averaging theorems for two-time scale systems, where the dynamics of the fast system are allowed to vary with the slow system. The results are applied to the Narendra-Valavani adaptive control algorithm, and estimates of the parameter convergence rates are obtained which do not rely on a linearization of the system around the equilibrium, and therefore are valid in a larger region in the parameter space.

Original language	English
Pages (from-to)	145-157
Number of pages	13
Journal	Systems and Control Letters
Volume	7
Issue number	3
DOIs	https://doi.org/10.1016/0167-6911(86)90108-8
Publication status	Published - Jun 1986

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10.1016/0167-6911(86)90108-8

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abstract = "The paper presents nonlinear averaging theorems for two-time scale systems, where the dynamics of the fast system are allowed to vary with the slow system. The results are applied to the Narendra-Valavani adaptive control algorithm, and estimates of the parameter convergence rates are obtained which do not rely on a linearization of the system around the equilibrium, and therefore are valid in a larger region in the parameter space.",

keywords = "Adaptive control, Averaging, Model reference, Nonlinear systems, Parameter convergence rates, Stability analysis",

author = "Marc Bodson and Shankar Sastry and Anderson, {Brian D.O.} and Iven Mareels and Bitmead, {Robert R.}",

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AU - Bodson, Marc

AU - Sastry, Shankar

AU - Anderson, Brian D.O.

AU - Mareels, Iven

AU - Bitmead, Robert R.

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N2 - The paper presents nonlinear averaging theorems for two-time scale systems, where the dynamics of the fast system are allowed to vary with the slow system. The results are applied to the Narendra-Valavani adaptive control algorithm, and estimates of the parameter convergence rates are obtained which do not rely on a linearization of the system around the equilibrium, and therefore are valid in a larger region in the parameter space.

AB - The paper presents nonlinear averaging theorems for two-time scale systems, where the dynamics of the fast system are allowed to vary with the slow system. The results are applied to the Narendra-Valavani adaptive control algorithm, and estimates of the parameter convergence rates are obtained which do not rely on a linearization of the system around the equilibrium, and therefore are valid in a larger region in the parameter space.

KW - Adaptive control

KW - Averaging

KW - Model reference

KW - Nonlinear systems

KW - Parameter convergence rates

KW - Stability analysis

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DO - 10.1016/0167-6911(86)90108-8

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VL - 7

SP - 145

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JO - Systems and Control Letters

JF - Systems and Control Letters

IS - 3

ER -

Nonlinear averaging theorems, and the determination of parameter convergence rates in adaptive control

Abstract

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