Neighboring extremal optimal control for mechanical systems on Riemannian manifolds

Anthony M. Bloch; Rohit  Gupta; Ilya V.  Kolmanovsky

doi:10.3934/jgm.2016007

Article Contents

2016, Volume 8, Issue 3: 257-272. Doi: 10.3934/jgm.2016007

This issue Previous Article Next Article Shape analysis on Lie groups with applications in computer animation

Neighboring extremal optimal control for mechanical systems on Riemannian manifolds

1.
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109
2.
Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109-2140

Received: September 30, 2015

Revised: May 31, 2016

Published: August 2016

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Abstract

In this paper, we extend neighboring extremal optimal control, which is well established for optimal control problems defined on a Euclidean space (see, e.g., [8]) to the setting of Riemannian manifolds. We further specialize the results to the case of Lie groups. An example along with simulation results is presented.

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Mathematics Subject Classification: Primary: 49J15, 49K40; Secondary: 37N35.

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