Optimal control on lie groups : the projection operator approach

A. Saccon, J. Hauser, A.P. Aguiar

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

28 Citaties (Scopus)

Uittreksel

Many nonlinear systems of practical interest evolve on Lie groups or on manifolds acted upon by Lie groups. Examples range from aircraft and underwater vehicles to quantum mechanical systems. In this paper, we develop an algorithm for solving continuous-time optimal control problems for systems evolving on (noncompact) Lie groups. This algorithm generalizes the projection operator approach for trajectory optimization originally developed for systems on vector spaces. Notions for generalizing system theoretic tools such as Riccati equations and linear and quadratic system approximations are developed. In this development, the covariant derivative of a map between two manifolds plays a key role in providing a chain rule for the required Lie group computations. An example optimal control problem on $SO(3)$ is provided to highlight implementation details and to demonstrate the effectiveness of the method
TaalEngels
Pagina's2230-2245
Aantal pagina's16
TijdschriftIEEE Transactions on Automatic Control
Volume58
Nummer van het tijdschrift9
DOI's
StatusGepubliceerd - 2013

Vingerafdruk

Lie groups
Riccati equations
Vector spaces
Mathematical operators
Nonlinear systems
Trajectories
Aircraft
Derivatives

Citeer dit

Saccon, A. ; Hauser, J. ; Aguiar, A.P./ Optimal control on lie groups : the projection operator approach. In: IEEE Transactions on Automatic Control. 2013 ; Vol. 58, Nr. 9. blz. 2230-2245
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Optimal control on lie groups : the projection operator approach. / Saccon, A.; Hauser, J.; Aguiar, A.P.

In: IEEE Transactions on Automatic Control, Vol. 58, Nr. 9, 2013, blz. 2230-2245.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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