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

拟议的项目涉及耗散固体的最佳控制。我们的出发点是考虑损伤效应和热弹塑性的材料模型。一个现代的解决方案理论，这样的系统与率无关的组件是基于所谓的平衡粘度解决方案，其存在性是通过粘性正则化和随后的通道中的粘度parameters.Within建议的项目，我们打算分析优化的损伤和热塑性变形过程下的解决方案的概念。除了最优控制的存在性之外，我们还主要研究了局部最优控制的粘性正则化的逼近性.速率相关的粘性问题本身具有物理意义，并且它们仍然是非光滑的，因为相关的控制-状态算子一般不是Gateaux可微的.此外，粘性问题作为一个有效的优化算法，在函数空间中的束方法的发展的基础。应用它，元素的次微分在克拉克意义上的粘性模型problems.By使用路径跟踪方法消失的粘度的基础上的方向导数，我们希望能够计算最优解，甚至相关的率无关的问题。

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.