Optimal control problem for deflection plate with crack. (English) Zbl 1266.53037
In control theory, sub-Riemannian spaces are regarded as standard model spaces. This paper considers a control problem where the state variable is defined as the solution of a variational inequality. This system describes the vertical displacement of points on a thin plate with the presence of cracks inside. In order to get the system of optimality for the control problem, the authors use a penalized problem and its reformulation as a Lagrangian problem. They prove the existence of a Lagrange multiplier to obtain a system of optimality to the exact problem via Lagrangian.
Reviewer: Peibiao Zhao (Nanjing)
MSC:
| 53C17 | Sub-Riemannian geometry |
| 22E30 | Analysis on real and complex Lie groups |
| 49J15 | Existence theories for optimal control problems involving ordinary differential equations |
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