基于粘性正则化的速率无关发展方程的最优控制
Optimal control of a rate-independent evolution equation via viscous regularization
摘要：
研究了由凸二次能量驱动的速率无关系统的最优控制。由于相关的解决方案映射是非光滑的，这样的控制问题的分析是具有挑战性的。为了得到最优性条件，我们研究了通过光滑的耗散潜力和通过添加一些粘性的问题的正则化。由此产生的正则化最优控制问题进行了分析。通过驱动正则化参数为零，我们得到了一个必要的最优性条件的原始，非光滑的问题。
英文摘要：
We study the optimal control of a rate-independent system that is driven by a convex, quadratic energy. Since the associated solution mapping is non-smooth, the analysis of such control problems is challenging. In order to derive optimality conditions, we study the regularization of the problem via a smoothing of the dissipation potential and via the addition of some viscosity. The resulting regularized optimal control problem is analyzed. By driving the regularization parameter to zero, we obtain a necessary optimality condition for the original, non-smooth problem.
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