TY - JOUR 
A1 - Delgado-Téllez, Marina
AU - Ibort, Alberto
AU - Rodríguez de la Pena, Thalía
T1 - Optimal Control Realizations of Lagrangian Systems with Symmetry
Y1 - 2011
SN - 02198878
UR - http://hdl.handle.net/11268/180
AB - 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 [1, 2]. 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.
KW - Optimal Control
KW - Variational Problems
KW - Lagrangian Systems With Symmetry
KW - Variational-Principles
KW - Physics
KW - Matemáticas
KW - Geometría
LA - eng
ER -