Optimal Control of Dissipative Solids: Viscosity Limits and Non-Smooth Algorithms

耗散固体的最优控制：粘度限制和非光滑算法

• 批准号: 314066412
• 负责人: Professor Dr. Roland Herzog
• 金额: --
• 依托单位: Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (IWR)
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/314066412?language=en
• 关键词: Optimal; Control; Dissipative; Solids; Viscosity

The proposed project concerns the optimal control of dissipative solids. Our point of departure is a thermodynamically consistent material model which takes into account damage effects as well as thermo-elastoplasticity. A modern solution theory for such systems with rate-independent components is based on so-called balanced viscosity solutions whose existence is proved by means of viscous regularization and a subsequent passage to the limit in the viscosity parameters.Within the proposed project, we intend to analyze the optimization of damage and thermo-plastic deformation processes under this solution concept. Besides the existence of optimal controls, we are mainly interested in the approximability of locally optimal controls by viscous regularization.The rate-dependent, viscous problems have a physical meaning in their own right, and they are still non-smooth in the sense that the associated control-to-state operator is, in general, not Gateaux differentiable. Moreover, the viscous problems serve as a basis for the development of an efficient optimization algorithm, a bundle method in function space. To apply it, elements of the subdifferential in the sense of Clarke are to be determined on the basis of directional derivatives for the viscous model problems.By using a path-following approach for vanishing viscosity, we expect to be able to compute optimal solutions even of the associated rate-independent problems.

拟议项目涉及耗散固体的优化控制。我们的出发点是热力学一致的材料模型，该模型考虑了损伤效应以及热弹塑性。这种具有速率无关分量的系统的现代解理论基于所谓的平衡粘度解，其存在通过粘性正则化和随后达到粘度参数极限来证明。在所提出的项目中，我们打算分析在此解概念下的损伤和热塑性变形过程的优化。除了最优控制的存在之外，我们主要感兴趣的是通过粘性正则化来逼近局部最优控制。速率相关的粘性问题本身就具有物理意义，并且它们仍然是非光滑的，因为相关的控制到状态算子通常不是 Gateaux 可微的。此外，粘性问题是开发高效优化算法（函数空间中的捆绑方法）的基础。为了应用它，克拉克意义上的次微分的元素将根据粘性模型问题的方向导数来确定。通过使用消失粘性的路径跟踪方法，我们期望能够计算甚至相关的速率无关问题的最优解。