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 ; Lovíšek, Ján
Applications of Mathematics, Tome 32 (1987), p. 315-331 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1987-01-01
Classification:  49A22,  49B22,  49J20,  49K20,  73H05,  73K10,  74G60,  74K20,  74P99 
@article{104262,
     author = {Igor Bock and Ivan Hlav\'a\v cek and J\'an Lov\'\i \v sek},
     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},
     volume = {32},
     year = {1987},
     pages = {315-331},
     zbl = {0639.73028},
     mrnumber = {0897835},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104262}
}

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) pp. 315-331. http://gdmltest.u-ga.fr/item/104262/

I. Bock I. Hlaváček J. Lovíšek On the optimal control problem governed by the equations of von Kárman, I. The homogeneous Dirichlet boundary conditions, Aplikace mat. 29 (1984), 303-314. (1984) | MR 0754082

I. Bock I. Hlaváček J. Lovíšek On the optimal control problem governed by the equations of von Kárman. II. Mixed boundary conditions, Aplikace mat. 30 (1985), 375-392. (1985) | MR 0806834

I. Hlaváček J. Neumann In homogeneous boundary value problems for the von Kárman equations. I, Aplikace mat. 19 (1974), 253-269. (1974) | MR 0377307

A. D. Joffe V. M. Tichomirov The theory of extremal problems, (in Russian). Moskva, Nauka 1974. (1974) | MR 0410502

O. John J. Nečas On the solvability of von Kárman equations, Aplikace mat. 20 (1975), 48-62. (1975) | MR 0380099

L. A. Ljusternik V. I. Sobolev The elements of functional analysis, (in Russian). Moskva, Nauka 1965. (1965) | MR 0209802

M. M. Vajnberg Variational methods of investigating nonlinear operators, (in Russian). Moskva, Gostechizdat 1956. (1956)

M. M. Vajnberg Variational method and a method of monotone operators, (in Russian). Moskva, Nauka 1972. (1972)