The objective of this paper is to interpret the approximate controllability of a semi-linear stochastic integrodifferential system with multiple delays and Poisson jumps in control in infinite-dimensional spaces. Sufficient conditions for the approximate controllability of semi-linear control system have been established. The results are obtained using the Banach fixed point theorem and the theory of resolvent operator developed in Grimmer [Resolvent operator for integral equations in Banach spaces, Trans. Am. Math. Soc. 273 (1982), pp. 333– 349.]. An example is introduced to show the effectiveness of the result.

中文翻译：

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控制中具有多重时滞和泊松跳跃的半线性随机积分微分系统的近似可控性

本文的目的是解释在无限维空间中具有多重延迟和泊松跳跃控制的半线性随机积分微分系统的近似可控性。建立了半线性控制系统近似可控性的充分条件。结果是使用 Banach 不动点定理和 Grimmer [Resolvent operator for integral equations in Banach spaces , Trans. 开发的解析算子理论获得的。是。数学。社会。273 (1982)，第 333-349 页]。举例说明结果的有效性。