Title :
Constrained variational principles on manifolds
Author :
Bloch, Anthony M. ; Crouch, Peter E.
Author_Institution :
Dept. of Math., Michigan Univ., Ann Arbor, MI, USA
Abstract :
We describe a geometric approach to finding the extremal equations for variational problems subject to nonlinear constraints on manifolds. This has applications to optimal control problems and extends earlier work. We formulate the problem on an appropriate vector bundle and show how to describe the extremal equations in terms of symplectic geometry on an appropriate reduced space
Keywords :
geometry; mechanical variables control; optimal control; variational techniques; vectors; constrained variational principles; extremal equations; geometric approach; manifolds; nonlinear constraints; optimal control problems; reduced space; symplectic geometry; variational problems; vector bundle; Geometry; Lagrangian functions; Manifolds; Mathematics; Mechanical systems; Nonlinear equations; Optimal control; Systems engineering and theory; Wheels;
Conference_Titel :
Decision and Control, 1999. Proceedings of the 38th IEEE Conference on
Conference_Location :
Phoenix, AZ
Print_ISBN :
0-7803-5250-5
DOI :
10.1109/CDC.1999.832736
