This article studies approximate controllability for a new class of semilinear control systems involving state-dependent delay in Hilbert space setting. We formulate some new sufficient conditions which ensure the existence of mild solution for the considered system via the Schauder fixed point theorem. We use the theory of fundamental solution and fractional powers of operator, to establish our major results. At last, two examples are constructed to substantiate the application of obtained results.

中文翻译：

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具有基本依赖状态的时滞的半线性系统的近似可控性

本文研究了一种新的半线性控制系统的近似可控性，该系统涉及希尔伯特空间设置中与状态有关的延迟。我们通过Schauder不动点定理制定了一些新的充分条件，以确保所考虑系统的温和解的存在。我们使用基本解和算子分数幂的理论来建立我们的主要结果。最后，构建了两个例子来证实所获得结果的应用。