WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 12, 2013
Optimal Control on Lie Groups: Theory and Applications
Author:
Abstract: In this paper we review Pontryagin’s Maximum Principle in its classical form, explain its geometric content and formulate it in a way which applies to control problems on arbitrary manifolds. It is then shown how this principle takes a particularly simple form in the case of left- or right-invariant control systems on Lie groups. Finally, we describe various application examples (from areas such as continuum mechanics, spacecraft attitude control and quantum spin systems) which show that the differential geometric version of Pontryagin’s Principle allows one to obtain solutions for concrete problems not easily found in other ways. The presentation is geared towards nonspecialists and strives to convey a feeling for the meaning and the applicability of the Maximum Principle rather than to present technical details.