论文标题
延迟的Caputo分数线性系统的区域可控性和最小能量控制
Regional Controllability and Minimum Energy Control of Delayed Caputo Fractional-Order Linear Systems
论文作者
论文摘要
我们通过使用标准Caputo导数来研究延迟分数控制系统的区域可控性问题。首先，我们回想起了几个基本结果，并介绍了所考虑的分数订单系统家族。之后，我们为具有控制延迟的分数系统制定了区域可控性的概念，并提供了一些重要的特性。我们的主要方法在于定义可实现的集合，这使我们能够证明精确和弱的可控性。此外，主要结果不仅包括具有可控性的结果，还包括一种强大的希尔伯特唯一方法，使我们能够解决最低能量最佳控制控制问题。确切地说，获得明确的控制，该控制将系统从初始给定状态驱动到具有最低能量的所需区域状态。举例说明了所获得的理论结果。
We study the regional controllability problem for delayed fractional control systems through the use of the standard Caputo derivative. First, we recall several fundamental results and introduce the family of fractional-order systems under consideration. Afterwards, we formulate the notion of regional controllability for fractional systems with control delays and give some of their important properties. Our main method consists in defining an attainable set, which allow us to prove exact and weak controllability. Moreover, main results include not only those of controllability but also a powerful Hilbert uniqueness method that allow us to solve the minimum energy optimal control control problem. Precisely, an explicit control is obtained that drives the system from an initial given state to a desired regional state with minimum energy. Examples are given to illustrate the obtained theoretical results.
