Geodesic
On the optimal control problem governed by the equations of von Kármán. III. The case of an arbitrary large perpendicular load
Applications of Mathematics, Tome 32 (1987) no. 4, pp. 315-331.

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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.
DOI : 10.21136/AM.1987.104262
Classification : 49A22, 49B22, 49J20, 49K20, 73H05, 73K10, 74G60, 74K20, 74P99
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 
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     title = {On the optimal control problem governed by the equations of von {K\'arm\'an.} {III.} {The} case of an arbitrary large perpendicular load},
     journal = {Applications of Mathematics},
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Bock, Igor; Hlaváček, Ivan; Lovíšek, Ján. On the optimal control problem governed by the equations of von Kármán. III. The case of an arbitrary large perpendicular load. Applications of Mathematics, Tome 32 (1987) no. 4, pp. 315-331. doi : 10.21136/AM.1987.104262. http://geodesic.mathdoc.fr/articles/10.21136/AM.1987.104262/

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