On the optimal control problem governed by the equations of von Kármán. III. The case of an arbitrary large perpendicular load

Bock, Igor, Hlaváček, Ivan, and Lovíšek, Ján. "On the optimal control problem governed by the equations of von Kármán. III. The case of an arbitrary large perpendicular load." Aplikace matematiky 32.4 (1987): 315-331. <http://eudml.org/doc/15503>.

@article{Bock1987,
abstract = {We shall deal with an optimal control problem for the deffection of a thin elastic plate. We consider the perpendicular load on the plate as the control variable. In contrast to the papers [1], [2], arbitrarily large loads are edmitted. As the unicity of a solution of the state equation is not guaranteed, we consider the cost functional defined on the set of admissible controls and states, and the state equation plays the role of the constraint. The existence of an optimal couple (i.e., control and state) is verified. By using Lagrange multipliers, some necessary optimality conditions are derived. A control problem with the cost functional involving all possible solutions of the state equation for arbitrary perpendicular load-control is investigated in the last part. The optimal control problem is solved via a sequence of penalized optimal control problems.},
author = {Bock, Igor, Hlaváček, Ivan, Lovíšek, Ján},
journal = {Aplikace matematiky},
keywords = {Lagrange multipliers; optimal control problem; system of von Kármán equations; deflection; thin elastic plate; perpendicular load; arbitrary large loads; existence proof; conditions of optimality; Lagrange multipliers; optimal control problem; system of von Kármán equations; deflection; thin elastic plate; perpendicular load; arbitrary large loads},
language = {eng},
number = {4},
pages = {315-331},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the optimal control problem governed by the equations of von Kármán. III. The case of an arbitrary large perpendicular load},
url = {http://eudml.org/doc/15503},
volume = {32},
year = {1987},
}

TY - JOUR
AU - Bock, Igor
AU - Hlaváček, Ivan
AU - Lovíšek, Ján
TI - On the optimal control problem governed by the equations of von Kármán. III. The case of an arbitrary large perpendicular load
JO - Aplikace matematiky
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 4
SP - 315
EP - 331
AB - We shall deal with an optimal control problem for the deffection of a thin elastic plate. We consider the perpendicular load on the plate as the control variable. In contrast to the papers [1], [2], arbitrarily large loads are edmitted. As the unicity of a solution of the state equation is not guaranteed, we consider the cost functional defined on the set of admissible controls and states, and the state equation plays the role of the constraint. The existence of an optimal couple (i.e., control and state) is verified. By using Lagrange multipliers, some necessary optimality conditions are derived. A control problem with the cost functional involving all possible solutions of the state equation for arbitrary perpendicular load-control is investigated in the last part. The optimal control problem is solved via a sequence of penalized optimal control problems.
LA - eng
KW - Lagrange multipliers; optimal control problem; system of von Kármán equations; deflection; thin elastic plate; perpendicular load; arbitrary large loads; existence proof; conditions of optimality; Lagrange multipliers; optimal control problem; system of von Kármán equations; deflection; thin elastic plate; perpendicular load; arbitrary large loads
UR - http://eudml.org/doc/15503
ER -