ABSTRACT

The paper deals with the optimal control of second-order viability problems for differential inclusions with endpoint constraint and duality. Based on the concept of infimal convolution and new approach to convex duality functions, we construct dual problems for discrete and differential inclusions and prove the duality results. It seems that the Euler–Lagrange type inclusions are ‘duality relations’ for both primary and dual problems. Finally, some special cases show the applicability of the general approach; duality in the control problem with second-order polyhedral DFIs and endpoint constraints defined by a polyhedral cone is considered.

中文翻译：

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具有端点约束和对偶的微分夹杂物的二阶生存力问题

摘要

本文讨论了具有端点约束和对偶性的微分夹杂物的二阶生存能力问题的优化控制。基于小卷积的概念和凸对偶函数的新方法，我们构造了离散和微分包含的对偶问题并证明了对偶结果。似乎 Euler-Lagrange 类型的包含对于主要问题和对偶问题都是“对偶关系”。最后，一些特殊情况表明了一般方法的适用性；考虑了具有二阶多面体 DFI 和由多面体锥定义的端点约束的控制问题中的对偶性。