理想塑性的最优控制部分II：位移跟踪
Optimal Control of Perfect Plasticity Part II: Displacement Tracking
摘要：
本文研究了率无关拟静态理想弹塑性系统的最优控制问题。其目标是通过指定的Dirichlet边界数据，作为控制变量，优化物体所占区域内的位移场。出现的最优化问题是不光滑的几个原因，特别是，因为控制到状态的映射不是单值的。因此，我们应用Yosida正则化，以获得一个单值的控制到状态的运营商。除了存在的最优解，他们的近似通过这种正规化的方法是这项工作的主要课题。事实证明，一个所谓的反向近似保证一个合适的恢复序列的存在下，只能显示在至少一个最优解的一个额外的平滑假设。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
