非凸积分-微分扫描过程的最优控制
Optimal control of nonconvex integro-differential sweeping processes
摘要：
本文致力于研究，在文献中的第一次，由积分-微分包含的Volterra型与不同类的控制功能，在非凸移动集，外部动态扰动，和整体部分的扫描动态扫描过程的最优控制问题。我们建立了最优解的存在性，然后得到了这类问题中广泛的一类局部极小的必要最优性条件。我们的方法来获得必要的最优性条件是基于离散逼近的方法结婚的基本建设和微积分规则的一阶和二阶变分分析和广义微分。所获得的必要的最优性条件表示完全的问题数据方面，并说明了非平凡的例子，包括应用程序的非常规电路的最优控制模型。
英文摘要：
This paper is devoted to the study, for the first time in the literature, of optimal control problems for sweeping processes governed by integro-differential inclusions of the Volterra type with different classes of control functions acting in nonconvex moving sets, external dynamic perturbations, and integral parts of the sweeping dynamics. We establish the existence of optimal solutions and then obtain necessary optimality conditions for a broad class of local minimizers in such problems. Our approach to deriving necessary optimality conditions is based on the method of discrete approximations married to basic constructions and calculus rules of first-order and second-order variational analysis and generalized differentiation. The obtained necessary optimality conditions are expressed entirely in terms of the problem data and are illustrated by nontrivial examples that include applications to optimal control models of non-regular electrical circuits.
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