论文标题
完美可塑性第二部分的最佳控制：位移跟踪
Optimal Control of Perfect Plasticity Part II: Displacement Tracking
论文作者
论文摘要
该论文涉及一个最佳控制问题，该问题由准静态弹性塑性性的速率无关系统控制。该目标是通过规定的Dirichlet边界数据来优化身体占据的域中的位移场，该数据用作控制变量。出现的优化问题是由于多种原因而不是平滑的，因为对照对状态映射不是单值。因此，我们应用Yosida正则化以获得单值对照对状态操作员。除了存在最佳解决方案之外，它们通过这种正则化方法的近似是这项工作的主要主题。事实证明，只有在至少一个最佳解决方案上的额外平滑度假设下才能显示出合适恢复序列存在的所谓反向近似。
The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is optimize the displacement field in the domain occupied by the body by means of prescribed Dirichlet boundary data, which serve as control variables. The arising optimization problem is nonsmooth for several reasons, in particular, since the control-to-state mapping is not single-valued. We therefore apply a Yosida regularization to obtain a single-valued control-to-state operator. Beside the existence of optimal solutions, their approximation by means of this regularization approach is the main subject of this work. It turns out that a so-called reverse approximation guaranteeing the existence of a suitable recovery sequence can only be shown under an additional smoothness assumption on at least one optimal solution.
