We consider an optimal control problem governed by a system of nonlinear difference equations. We obtain the existence of the optimal control as well as first-order optimality conditions of Pontryagin type by using the Dubovitskii–Milyutin formalism. Also, we give the necessary and sufficient conditions for global optimality.

中文翻译：

---

离散时间控制问题的最优条件

我们考虑由非线性差分方程组控制的最优控制问题。我们通过使用 Dubovitskii-Milyutin 形式主义获得了 Pontryagin 类型的最优控制和一阶最优条件的存在性。此外，我们给出了全局最优的充要条件。