| Title:
|
On the optimal control problem governed by the equations of von Kármán. III. The case of an arbitrary large perpendicular load (English) |
| Author:
|
Bock, Igor |
| Author:
|
Hlaváček, Ivan |
| Author:
|
Lovíšek, Ján |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1987 |
| Pages:
|
315-331 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Lagrange multipliers |
| Keyword:
|
optimal control problem |
| Keyword:
|
system of von Kármán equations |
| Keyword:
|
deflection |
| Keyword:
|
thin elastic plate |
| Keyword:
|
perpendicular load |
| Keyword:
|
arbitrary large loads |
| Keyword:
|
existence proof |
| Keyword:
|
conditions of optimality |
| MSC:
|
49A22 |
| MSC:
|
49B22 |
| MSC:
|
49J20 |
| MSC:
|
49K20 |
| MSC:
|
73H05 |
| MSC:
|
73K10 |
| MSC:
|
74G60 |
| MSC:
|
74K20 |
| MSC:
|
74P99 |
| idZBL:
|
Zbl 0639.73028 |
| idMR:
|
MR0897835 |
| DOI:
|
10.21136/AM.1987.104262 |
| . |
| Date available:
|
2008-05-20T18:32:49Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104262 |
| . |
| Reference:
|
[1] 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. MR 0754082 |
| Reference:
|
[2] 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. MR 0806834 |
| Reference:
|
[3] I. Hlaváček J. Neumann: In homogeneous boundary value problems for the von Kárman equations. I.Aplikace mat. 19 (1974), 253-269. MR 0377307 |
| Reference:
|
[4] A. D. Joffe V. M. Tichomirov: The theory of extremal problems.(in Russian). Moskva, Nauka 1974. MR 0410502 |
| Reference:
|
[5] O. John J. Nečas: On the solvability of von Kárman equations.Aplikace mat. 20 (1975), 48-62. MR 0380099 |
| Reference:
|
[6] L. A. Ljusternik V. I. Sobolev: The elements of functional analysis.(in Russian). Moskva, Nauka 1965. MR 0209802 |
| Reference:
|
[7] M. M. Vajnberg: Variational methods of investigating nonlinear operators.(in Russian). Moskva, Gostechizdat 1956. |
| Reference:
|
[8] M. M. Vajnberg: Variational method and a method of monotone operators.(in Russian). Moskva, Nauka 1972. |
| . |
