In the article, we derive an existence theorem for a Bolza problem described by a nonlinear integro‐differential system of Volterra type. We use an approach based on the lower closure theorem for orientor fields due to Cesari and measurable selection theorem of Fillipov type due to Rockafellar. Paper is a continuation of [D. Idczak, S. Walczak, Necessary optimality conditions for an integro‐differential Bolza problem via Dubovitskii‐Miljutin method, DCDS‐B 24 (5) (2019), 2281‐2292; DOI:10.3934/dcdsb.2019095].

中文翻译：

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积分-微分Bolza问题的最优控制的存在

在本文中，我们推导了由Volterra型非线性积分微分系统描述的Bolza问题的存在性定理。由于切萨里（Cesari），我们使用基于下封闭定理的定向场；由于洛克菲拉尔（Rockafellar），我们使用了可测的菲利波夫选择定理。纸是[D. Idczak，S.Walczak，通过Dubovitskii-Miljutin方法求解积分微分Bolza问题的必要最优条件，DCDS-B 24（5）（2019），2281-2292; DOI：10.3934 / dcdsb.2019095]。