Delayed Feedback Asymptotic Stabilization of Rigid Body Attitude Motion for Large Rotations

Ehsan Samiei; Maziar Izadi; Amit K. Sanyal; Eric A. Butcher

doi:10.1016/j.ifacol.2015.09.357

Delayed Feedback Asymptotic Stabilization of Rigid Body Attitude Motion for Large Rotations

Ehsan Samiei, Maziar Izadi, Amit K. Sanyal, Eric A. Butcher

Department of Mechanical & Aerospace Engineering

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

3 Scopus citations

Abstract

The delayed feedback control of rigid body attitude motion is addressed where there is an unknown time delay in the feedback measurement. The attitude motion is described on the tangent bundle TSO(3) to globally and uniquely represent the orientation of the rigid body, while a continuous nonlinear delayed feedback control law is proposed for local asymptotic stabilization on TSO(3). For this purpose, we introduce a notion based on the Lyapunov technique, which combines the Morse-Lyapunov method with Lyapunov-Krasovskii technique to yield a suitable Morse-Lyapunov-Krasovskii (M-L-K) functional, from which the stability conditions and proper control gain matrices are obtained in terms of linear matrix inequalities (LMIs). Simulations illustrate the performance of the proposed control scheme.

Original language	English (US)
Pages (from-to)	81-86
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	48
Issue number	12
DOIs	https://doi.org/10.1016/j.ifacol.2015.09.357
State	Published - 2015

Keywords

Attitude control
LMIs
Lyapunov-Krasovskii functional
time-delayed system

ASJC Scopus subject areas

Control and Systems Engineering

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10.1016/j.ifacol.2015.09.357

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@article{e7c0542fe9464c1a86b16dac2affd344,

title = "Delayed Feedback Asymptotic Stabilization of Rigid Body Attitude Motion for Large Rotations",

abstract = "The delayed feedback control of rigid body attitude motion is addressed where there is an unknown time delay in the feedback measurement. The attitude motion is described on the tangent bundle TSO(3) to globally and uniquely represent the orientation of the rigid body, while a continuous nonlinear delayed feedback control law is proposed for local asymptotic stabilization on TSO(3). For this purpose, we introduce a notion based on the Lyapunov technique, which combines the Morse-Lyapunov method with Lyapunov-Krasovskii technique to yield a suitable Morse-Lyapunov-Krasovskii (M-L-K) functional, from which the stability conditions and proper control gain matrices are obtained in terms of linear matrix inequalities (LMIs). Simulations illustrate the performance of the proposed control scheme.",

keywords = "Attitude control, LMIs, Lyapunov-Krasovskii functional, time-delayed system",

author = "Ehsan Samiei and Maziar Izadi and Sanyal, {Amit K.} and Butcher, {Eric A.}",

note = "Funding Information: ★ Financial support from the National Science Foundation under ★ Financial support from the National Science Foundation under GrFainntaNncoi.alCMsuMppIo-1rt13f1r6o4m6 itshegraNtaetfuiolnlyalacSkcnieonwcleedFgoeudn. dation under GrFainntaNncoi.alCMsuMppIo-1rt13f1r6o4m6 itshegraNtaetfuiolnlyalacSkcnieonwcleedFgoeudn. dation under Grant No. CMMI-1131646 is gratefully acknowledged. Funding Information: Financial fiΦpport Ψrom the National Science FoΦnffiation Φnffier Grant No. CMMI-1131646 ifi grateΨΦlly acknowl-effigeffi.",

year = "2015",

doi = "10.1016/j.ifacol.2015.09.357",

language = "English (US)",

volume = "48",

pages = "81--86",

journal = "IFAC-PapersOnLine",

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AU - Samiei, Ehsan

AU - Izadi, Maziar

AU - Sanyal, Amit K.

AU - Butcher, Eric A.

N1 - Funding Information: ★ Financial support from the National Science Foundation under ★ Financial support from the National Science Foundation under GrFainntaNncoi.alCMsuMppIo-1rt13f1r6o4m6 itshegraNtaetfuiolnlyalacSkcnieonwcleedFgoeudn. dation under GrFainntaNncoi.alCMsuMppIo-1rt13f1r6o4m6 itshegraNtaetfuiolnlyalacSkcnieonwcleedFgoeudn. dation under Grant No. CMMI-1131646 is gratefully acknowledged. Funding Information: Financial fiΦpport Ψrom the National Science FoΦnffiation Φnffier Grant No. CMMI-1131646 ifi grateΨΦlly acknowl-effigeffi.

PY - 2015

Y1 - 2015

N2 - The delayed feedback control of rigid body attitude motion is addressed where there is an unknown time delay in the feedback measurement. The attitude motion is described on the tangent bundle TSO(3) to globally and uniquely represent the orientation of the rigid body, while a continuous nonlinear delayed feedback control law is proposed for local asymptotic stabilization on TSO(3). For this purpose, we introduce a notion based on the Lyapunov technique, which combines the Morse-Lyapunov method with Lyapunov-Krasovskii technique to yield a suitable Morse-Lyapunov-Krasovskii (M-L-K) functional, from which the stability conditions and proper control gain matrices are obtained in terms of linear matrix inequalities (LMIs). Simulations illustrate the performance of the proposed control scheme.

AB - The delayed feedback control of rigid body attitude motion is addressed where there is an unknown time delay in the feedback measurement. The attitude motion is described on the tangent bundle TSO(3) to globally and uniquely represent the orientation of the rigid body, while a continuous nonlinear delayed feedback control law is proposed for local asymptotic stabilization on TSO(3). For this purpose, we introduce a notion based on the Lyapunov technique, which combines the Morse-Lyapunov method with Lyapunov-Krasovskii technique to yield a suitable Morse-Lyapunov-Krasovskii (M-L-K) functional, from which the stability conditions and proper control gain matrices are obtained in terms of linear matrix inequalities (LMIs). Simulations illustrate the performance of the proposed control scheme.

KW - Attitude control

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KW - Lyapunov-Krasovskii functional

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