We consider the Seierstad sufficiency theorem in comparison with the Mangasarian and Arrow sufficiency theorems for optimal control problems with infinite time horizon. Both finite and infinite values of the objective functional are allowed, since the concepts of overtaking and weakly overtaking optimality are implied. We extend the conditions under which the Seierstad sufficiency theorem can be applied and provide appropriate examples. The sufficient conditions are shown to be both necessary and sufficient when the Hamiltonian is linear with respect to state and control. We obtain a new form of sufficient optimality conditions in the case when the Hamiltonian is neither concave nor differentiable with respect to control.

中文翻译：

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无限视界最优控制问题的充分最优条件

我们将Seierstad充分性定理与Mangasarian和Arrow充分性定理进行比较，以解决无限时间范围内的最优控制问题。目标函数的有限值和无限值都允许，因为暗示了超越和弱超越最优的概念。我们扩展了可以应用Seierstad充分性定理的条件，并提供了适当的示例。当哈密顿量关于状态和控制是线性的时，充分条件被证明既必要又充分。当哈密顿量在控制上既不是凹面也不是可微分的情况下，我们获得了具有充分最优性条件的新形式。