基于拟切条件的随机半线性控制系统生存性判据
A Criterion for the Viability of Stochastic Semilinear Control Systems via the Quasi-Tangency Condition
摘要：
本文研究了实可分希尔伯特空间上随机半线性控制系统生存的一个判据。利用随机拟切的概念，给出了这类问题的充要条件。因此，我们证明了随机线性控制系统的近似生存性和生存性是一致的。我们得到南云的随机定理，我们提出了一种方法，允许提供明确的标准，光滑集的生存能力。我们分析了表征单位球生存能力的条件。本文概括了最近的结果，从确定性的框架。
英文摘要：
In this paper we study a criterion for the viability of stochastic semilinear control systems on a real, separable Hilbert space. The necessary and sufficient conditions are given using the notion of stochastic quasi-tangency. As a consequence, we prove that approximate viability and the viability property coincide for stochastic linear control systems. We obtain Nagumo's stochastic theorem and we present a method allowing to provide explicit criteria for the viability of smooth sets. We analyze the conditions characterizing the viability of the unit ball. The paper generalizes recent results from the deterministic framework.
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