Approximate controllability of impulsive semilinear evolution equations in Hilbert spaces

Several dynamical systems in fields such as engineering, chemistry, biology, and physics show impulsive behaviour by reason of unexpected changes at specific times. These behaviours are described by differential systems under impulse effects. The current paper examines approximate controllability for semi-linear impulsive differential and neutral differential equations in Hilbert spaces. By applying a fixed-point method and semigroup theory, a new sufficient condition is provided for the (A-controllability) approximate controllability of neutral and impulsive differential equations (IDEs). To demonstrate the value of the suggested consequences, three examples are presented, offering improvements over some recent findings.

工程、化学、生物学以及物理学等领域的诸多动力系统，会因特定时刻的突发变化而呈现脉冲行为。这类行为可通过受脉冲效应影响的微分系统进行描述。本文针对希尔伯特空间中的半线性脉冲微分方程与中立型微分方程，研究其近似可控性问题。借助不动点方法与半群理论，本文为中立型与脉冲微分方程（IDEs）的（A可控性(A-controllability)）近似可控性提供了全新的充分条件。为验证所提结论的应用价值，本文给出三个算例，相较于部分近期研究成果，本研究的结论实现了一定的改进。