The main concern of this paper is to investigate sensitivity properties of parametric evolution systems of first order involving a general class of nonconvex functions. Using recent results on the stability of the subdifferentials, with respect to the Gamma convergence, of the associated sequence of subsmooth or semiconvex functions, we give some continuity properties of the solution set associated to these problems. The particular case of the parametric sweeping process involving uniformly subsmooth or uniformly prox-regular sets is studied in details. As an application, we study the sensitivity analysis of the generalized Bolza/Mayer problem governed by a nonsmooth dynamic of a sweeping process type.

中文翻译：

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参数非凸演化包含物的灵敏度性质及其在最优控制问题中的应用

本文的主要关注点是研究涉及一类非凸函数的一阶参数演化系统的灵敏度特性。使用最近的关于亚平滑或半凸函数的相关序列的与Gamma收敛有关的微分稳定性的结果，我们给出了与这些问题相关的解集的某些连续性。详细研究了涉及均匀次光滑或均匀近似正则集的参数清扫过程的特殊情况。作为应用，我们研究了广义Bolza / Mayer问题的敏感性分析，该问题受清扫过程类型的非光滑动力控制。