Mathematics – Optimization and Control
Scientific paper
2012-03-09
Int. J. Geom. Meth. Mod. Phys., 8 (7) 1-25 (2011)
Mathematics
Optimization and Control
Scientific paper
A new relation among a class of optimal control systems and Lagrangian systems with symmetry is discussed. It will be shown that a family of solutions of optimal control systems whose control equation are obtained by means of a group action are in correspondence with the solutions of a mechanical Lagrangian system with symmetry. This result also explains the equivalence of the class of Lagrangian systems with symmetry and optimal control problems discussed in \cite{Bl98}, \cite{Bl00}. The explicit realization of this correspondence is obtained by a judicious use of Clebsch variables and Lin constraints, a technique originally developed to provide simple realizations of Lagrangian systems with symmetry. It is noteworthy to point out that this correspondence exchanges the role of state and control variables for control systems with the configuration and Clebsch variables for the corresponding Lagrangian system. These results are illustrated with various simple applications.
Delgado-Tellez M.
Ibort Alberto
La Peña Thalia Rodriguez de
No associations
LandOfFree
Optimal Control Realizations of Lagrangian Systems with Symmetry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Optimal Control Realizations of Lagrangian Systems with Symmetry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Optimal Control Realizations of Lagrangian Systems with Symmetry will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-488125