This paper investigates the time optimal control for a class of non-instantaneous impulsive Clarke subdifferential type stochastic evolution inclusions in Hilbert spaces. We focus first on the existence of mild solutions for these systems by using the measure of non-compactness and a fixed-point theorem wth the properties of Clarke subdifferential. Then, the existence of time optimal control of governed by stochastic control systems is also obtained. We do not assume that the evolution operator and the values of multi-valued map are compact. Finally, an example is given to illustrate the effectiveness of the results.

中文翻译：

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Hilbert空间中Clarke次微分型随机演化包含的时间最优控制

本文研究了希尔伯特空间中一类非瞬时脉冲克拉克亚微分型随机演化包含物的时间最优控制。我们首先通过使用非紧致性的度量和具有Clarke次微分性质的不动点定理，着眼于这些系统的温和解的存在。然后，还获得了由随机控制系统控制的时间最优控制的存在。我们不认为进化算子和多值映射的值是紧凑的。最后，给出一个例子来说明结果的有效性。