Cut Locus and Optimal Synthesis in Sub-Riemannian Problem on the Lie Group SH(2)

Yasir Awais Butt; Yuri L. Sachkov; Aamer Iqbal Bhatti

doi:10.1007/s10883-016-9337-4

Cut Locus and Optimal Synthesis in Sub-Riemannian Problem on the Lie Group SH(2)

Yasir Awais Butt^*, Yuri L. Sachkov, Aamer Iqbal Bhatti

^*Corresponding author for this work

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

18 Scopus citations

Abstract

Global optimality analysis in sub-Riemannian problem on the Lie group SH(2) is considered. We cutout open dense domains in the preimage and in the image of the exponential mapping based on the description of Maxwell strata. We then prove that the exponential mapping restricted to these domains is a diffeomorphism. Based on the proof of diffeomorphism, the cut time, i.e., time of loss of global optimality, is computed on SH(2). We also consider the global structure of the exponential mapping and obtain an explicit description of cut locus and optimal synthesis.

Original language	English
Pages (from-to)	155-195
Number of pages	41
Journal	Journal of Dynamical and Control Systems
Volume	23
Issue number	1
DOIs	https://doi.org/10.1007/s10883-016-9337-4
State	Published - 1 Jan 2017
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2016, Springer Science+Business Media New York.

Keywords

Conjugate time
Cut time
Maxwell points
Optimal synthesis
Special hyperbolic group SH(2)
Sub-Riemannian geometry

ASJC Scopus subject areas

Control and Systems Engineering
Algebra and Number Theory
Numerical Analysis
Control and Optimization

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Cite this

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title = "Cut Locus and Optimal Synthesis in Sub-Riemannian Problem on the Lie Group SH(2)",

abstract = "Global optimality analysis in sub-Riemannian problem on the Lie group SH(2) is considered. We cutout open dense domains in the preimage and in the image of the exponential mapping based on the description of Maxwell strata. We then prove that the exponential mapping restricted to these domains is a diffeomorphism. Based on the proof of diffeomorphism, the cut time, i.e., time of loss of global optimality, is computed on SH(2). We also consider the global structure of the exponential mapping and obtain an explicit description of cut locus and optimal synthesis.",

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author = "Butt, {Yasir Awais} and Sachkov, {Yuri L.} and Bhatti, {Aamer Iqbal}",

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AU - Butt, Yasir Awais

AU - Sachkov, Yuri L.

AU - Bhatti, Aamer Iqbal

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Global optimality analysis in sub-Riemannian problem on the Lie group SH(2) is considered. We cutout open dense domains in the preimage and in the image of the exponential mapping based on the description of Maxwell strata. We then prove that the exponential mapping restricted to these domains is a diffeomorphism. Based on the proof of diffeomorphism, the cut time, i.e., time of loss of global optimality, is computed on SH(2). We also consider the global structure of the exponential mapping and obtain an explicit description of cut locus and optimal synthesis.

AB - Global optimality analysis in sub-Riemannian problem on the Lie group SH(2) is considered. We cutout open dense domains in the preimage and in the image of the exponential mapping based on the description of Maxwell strata. We then prove that the exponential mapping restricted to these domains is a diffeomorphism. Based on the proof of diffeomorphism, the cut time, i.e., time of loss of global optimality, is computed on SH(2). We also consider the global structure of the exponential mapping and obtain an explicit description of cut locus and optimal synthesis.

KW - Conjugate time

KW - Cut time

KW - Maxwell points

KW - Optimal synthesis

KW - Special hyperbolic group SH(2)

KW - Sub-Riemannian geometry

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SN - 1079-2724

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JO - Journal of Dynamical and Control Systems

JF - Journal of Dynamical and Control Systems

IS - 1

ER -

Cut Locus and Optimal Synthesis in Sub-Riemannian Problem on the Lie Group SH(2)

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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