Optimal attitude control of a rigid body
type: Item
instance of: scholarly article
title: Optimal attitude control of a rigid body
zbMATH Open document ID: 0884.70036
DOI: 10.1007/BF01182474
published in: Applied Mathematics and Optimization
publication date: 1998-03-18T00:00:00Z
review text: The control of satellite motion is studied under the condition that the cost functional measuring the overall angular velocity is minimized. The author uses the Jurdjevic's geometric method quoted in the bibliography. This technique can be considered as classical calculus of variations applied to optimal control problems without constraints, but it can be also formulated for control problems on arbitrary manifolds and presented in coordinate-free language. The evolution state is modelled by a differential equation in the space of nonlinear states using the angular velocities \(\omega_k\) of rotations around the principal axes of the body. The Pontryagin's maximum principle allows to determine optimal trajectories and integral curves at a certain time -- an invariant Hamiltonian vector field. The optimal angular velocities \(\omega_k^*(t)\) can then be found by means of Poisson brackets applied to a system of differential equations. The unknown optimal torques can be determined by using the Euler's equations. Finally, the author presents eight particular cases together with numerical results.
reviewed by: Ştefan Zanfir
Mathematics Subject Classification ID: 70Q05
Mathematics Subject Classification ID: 70E15
zbMATH DE Number: 897234
zbMATH Keywords: satellite motion
zbMATH Keywords: geometric control theory
zbMATH Keywords: cost functional
zbMATH Keywords: angular velocity
zbMATH Keywords: Jurdjevic's geometric method
zbMATH Keywords: Pontryagin's maximum principle
zbMATH Keywords: integral curves
zbMATH Keywords: invariant Hamiltonian vector field
zbMATH Keywords: Poisson brackets
zbMATH Keywords: optimal torques
zbMATH Keywords: Euler's equations
author: Karlheinz Spindler
MaRDI profile type: Publication
cites work: Q4174811
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full work available at URL: https://doi.org/10.1007/bf01182474
OpenAlex ID: W2055127277
description: scientific article; zbMATH DE number 897234