On the optimal control of implicit systems

Petit, P.. "On the optimal control of implicit systems." ESAIM: Control, Optimisation and Calculus of Variations 3 (2010): 49-81. <http://eudml.org/doc/197363>.

@article{Petit2010,
abstract = { In this paper we consider the well-known implicit Lagrange problem: find a trajectory solution of an underdetermined implicit differential equation, satisfying some boundary conditions and which is a minimum of the integral of a Lagrangian. In the tangent bundle of the surrounding manifold X, we define the geometric framework of q-pi- submanifold. This is an extension of the geometric framework of pi- submanifold, defined by Rabier and Rheinboldt for determined implicit differential equations, to underdetermined implicit differential equations. With this geometric framework we define a class of well-posed implicit differential equations for which we locally obtain, by means of a reduction procedure, a controlled vector field on a submanifold W of the surrounding manifold X. We then show that the implicit Lagrange problem leads to, locally, an explicit optimal control problem on the submanifold W for which the Pontryagin maximum principle is naturally used. },
author = {Petit, P.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Implicit systems; optimal control; Pontryagin maximum principle; manifold; submanifold; subimmersion .; --submanifolds; implicit differential equations},
language = {eng},
month = {3},
pages = {49-81},
publisher = {EDP Sciences},
title = {On the optimal control of implicit systems},
url = {http://eudml.org/doc/197363},
volume = {3},
year = {2010},
}

TY - JOUR
AU - Petit, P.
TI - On the optimal control of implicit systems
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 3
SP - 49
EP - 81
AB - In this paper we consider the well-known implicit Lagrange problem: find a trajectory solution of an underdetermined implicit differential equation, satisfying some boundary conditions and which is a minimum of the integral of a Lagrangian. In the tangent bundle of the surrounding manifold X, we define the geometric framework of q-pi- submanifold. This is an extension of the geometric framework of pi- submanifold, defined by Rabier and Rheinboldt for determined implicit differential equations, to underdetermined implicit differential equations. With this geometric framework we define a class of well-posed implicit differential equations for which we locally obtain, by means of a reduction procedure, a controlled vector field on a submanifold W of the surrounding manifold X. We then show that the implicit Lagrange problem leads to, locally, an explicit optimal control problem on the submanifold W for which the Pontryagin maximum principle is naturally used.
LA - eng
KW - Implicit systems; optimal control; Pontryagin maximum principle; manifold; submanifold; subimmersion .; --submanifolds; implicit differential equations
UR - http://eudml.org/doc/197363
ER -