希尔伯特空间中二阶发展微分包含的近似能控性
Approximate controllability of second-order evolution differential inclusions in Hilbert spaces
摘要：
本文考虑了希尔伯特空间中一类二阶发展微分包含.研究了一类二阶控制系统的近似能控性。首先，我们在希尔伯特空间中建立了一类二阶发展微分包含的近似能控性的充分条件。我们利用Bohnenblust-Karlin的不动点定理证明了我们的主要结果。进一步，我们将结果推广到研究了非局部条件下的近似能控性概念，并将结果推广到研究了非局部条件下脉冲控制系统的近似能控性。最后给出一个例子来说明我们的主要结果。
英文摘要：
In this paper, we consider a class of second-order evolution differential inclusions in Hilbert spaces. This paper deals with the approximate controllability for a class of second-order control systems. First, we establish a set of sufficient conditions for the approximate controllability for a class of second-order evolution differential inclusions in Hilbert spaces. We use Bohnenblust-Karlin's fixed point theorem to prove our main results. Further, we extend the result to study the approximate controllability concept with nonlocal conditions and extend the result to study the approximate controllability for impulsive control systems with nonlocal conditions. An example is also given to illustrate our main results.
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