The paper deals with the optimal control problem described by second order evolution differential inclusions; to this end first we use an auxiliary problem with second order discrete and discrete-approximate inclusions. Then applying infimal convolution concept of convex functions, step by step we construct the dual problems for discrete, discrete-approximate and differential inclusions and prove duality results. It seems that the Euler-Lagrange type inclusions are "duality relations" for both primary and dual problems and that the dual problem for discrete-approximate problem make a bridge between them. At the end of the paper duality in problems with second order linear discrete and continuous models and model of control problem with polyhedral DFIs are considered.

中文翻译：

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具有二阶演化微分包含的凸最优控制问题的小卷积和对偶

本文讨论了由二阶演化微分包含描述的最优控制问题。为此，我们首先使用带有二阶离散和离散近似包含的辅助问题。然后运用凸函数的极小卷积概念，逐步构造离散，离散近似和微分包含的对偶问题，并证明对偶结果。看来欧拉-拉格朗日型夹杂物对主要问题和对偶问题都是“对偶关系”，而离散近似问题的对偶问题在两者之间架起了桥梁。在本文的最后，考虑了具有二阶线性离散和连续模型的问题的对偶性以及具有多面DFI的控制问题的模型。