Intrinsic optimal control for mechanical systems on Lie group
type: Item
instance of: scholarly article
title: Intrinsic optimal control for mechanical systems on Lie group
zbMATH Open document ID: 1401.49033
DOI: 10.1155/2017/6302430
author: Chao Liu
author: Shengjing Tang
author: Jie Guo
published in: Advances in Mathematical Physics
publication date: 2018-10-23T00:00:00Z
review text: Summary: The intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal problem in the geometric viewpoint, a simplified nominal system on Lie group with an extra feedback loop is presented. With geodesic distance and Riemann metric on Lie group integrated into the cost function, a dynamic programming approach is employed and an analytical solution of the optimal problem on Lie group is obtained via the Hamilton-Jacobi-Bellman equation. For a special case on \(\mathbf{SO}(3)\), the intrinsic optimal control method is used for a quadrotor rotation control problem and simulation results are provided to show the control performance.
Mathematics Subject Classification ID: 49L20
Mathematics Subject Classification ID: 93C85
Mathematics Subject Classification ID: 49N90
Mathematics Subject Classification ID: 93B27
Mathematics Subject Classification ID: 93B52
Mathematics Subject Classification ID: 90C39
Mathematics Subject Classification ID: 70Q05
Mathematics Subject Classification ID: 93B25
zbMATH DE Number: 6962649
zbMATH Keywords: optimal control
zbMATH Keywords: mechanical systems
zbMATH Keywords: Lie group
zbMATH Keywords: geometric optimal control
zbMATH Keywords: feedback loop
zbMATH Keywords: dynamic programming
zbMATH Keywords: quadrotor rotation control
MaRDI profile type: Publication
Wikidata QID: Q59142454
full work available at URL: https://doi.org/10.1155/2017/6302430
OpenAlex ID: W2734506151
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description: scientific article; zbMATH DE number 6962649