Optimal Control on Lie Groups: The Projection Operator Approach

• Type: Article in International Scientific Journal
• Date: 2013

Authors

Alessandro Saccon (Author) Other; John Hauser (Author) Other; Pedro Aguiar, AP (Author) FEUP

Journal

Title: IEEE Transactions on Automatic Control

Vol. 58 No. 4

Pages: 2230-2245

ISSN: 0018-9286

Publisher: IEEE

Indexing

ISI Web of Knowledge - 29 Citations

Scopus - 34 Citations

Scientific classification

FOS: Engineering and technology > Electrical engineering, Electronic engineering, Information engineering

Other information

Authenticus ID: P-006-7SE

DOI: 10.1109/tac.2013.2258817

Abstract (EN): 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 is provided to highlight implementation details and to demonstrate the effectiveness of the method.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 16