耦合反应扩散系统的有限时间同步

发布时间：2018-06-16 22:57

本文选题：耦合反应扩散系统 + 时滞　；参考：《哈尔滨工业大学》2017年硕士论文

【摘要】：复杂网络存在于生活的方方面面,如经济网络、交通网以及电力网。许多物理及化学反应,如核反应、地下水渗流和热传导等,它们系统的状态同时依赖于时间和空间,当这类系统所处的空间是非均匀的时候,扩散现象不可避免地发生。因为同步问题具有广泛的应用价值,近几十年来已经成为了许多学者研究的热点。对于同步的分类,根据系统实现同步状态的时间可以分为渐近同步和有限时间同步。相较于渐近同步,有限时间同步因为实现同步状态需要的时间有限且可计算而在工程等领域中受到高度重视。由于系统中存在大量需要被传输的数据,而系统各个节点之间有限的传输速度以及系统各个节点本身的处理器速度限制使得时滞不可避免的发生。本文将分别通过施加全域控制、边界控制以及牵制控制的方法来使系统在有限时间内达到同步状态。本文针对具有变时滞的耦合反应扩散系统,研究了有限时间同步问题,通过对具有变时滞的反应扩散系统施加全域控制器,利用Lyapunov-Krasovskii泛函方法并结合线性矩阵不等式技巧,得到了系统实现有限时间同步的充分性判据。同时针对具有常时滞耦合反应扩散系统的有限时间同步问题给出了简要说明。最后,给出了相应的算例仿真,演示了所得理论结果的有效性。接着研究了耦合反应扩散系统的有限时间边界控制问题,分别研究了不具有时滞的耦合反应扩散系统有限时间边界控制以及具有时滞的耦合反应扩散系统有限时间边界控制。对两种耦合反应扩散系统的有限时间同步问题,分别针对混合边界和Neumann边界设计了不同的控制器,得到了系统实现有限时间同步的充分性判据。最后,给出了相应的算例,演示了所得理论结果的有效性。然后讨论了自适应耦合反应扩散系统有限时间牵制控制问题。通过使用自适应技巧以及设计牵制控制器,得到了使系统实现有限时间同步的充分性判据。最后,给出了相应的算例,演示了所得理论结果的有效性。
[Abstract]:Complex networks exist in all aspects of life, such as economic networks, transportation networks and power networks. Many physical and chemical reactions, such as nuclear reactions, groundwater seepage and heat conduction, depend on both time and space for the state of their systems. Because of its wide application value, synchronization has become a hot topic for many scholars in recent decades. For the classification of synchronization, it can be divided into asymptotic synchronization and finite time synchronization according to the time of realizing synchronization. Compared with asymptotic synchronization, finite time synchronization has attracted great attention in engineering and other fields because of the limited time required to realize the synchronization state and its computability. Due to the large amount of data needed to be transmitted in the system, the limited transmission speed between each node of the system and the processor speed limit of each node in the system make the delay inevitable. In this paper, global control, boundary control and containment control are applied to make the system synchronize in finite time. In this paper, the finite time synchronization problem is studied for coupled reaction-diffusion systems with time-varying delays. By applying a global controller to the reaction-diffusion systems with time-varying delays, the Lyapunov-Krasovskii functional method and the techniques of linear matrix inequality (LMI) are used. A sufficient criterion for realizing finite time synchronization is obtained. At the same time, the finite time synchronization of coupled reaction diffusion systems with constant delay is briefly described. Finally, an example is given to demonstrate the effectiveness of the theoretical results. Then the finite time boundary control problem of coupled reaction diffusion systems is studied. The finite time boundary control of coupled reaction diffusion systems without time delay and the finite time boundary control of coupled reaction diffusion systems with time delay are studied respectively. For two kinds of coupled reaction-diffusion systems, different controllers are designed for the mixed boundary and Neumann boundary respectively, and the sufficient criteria for realizing the finite time synchronization are obtained. Finally, an example is given to demonstrate the validity of the theoretical results. Then the finite time control problem of adaptive coupled reaction diffusion system is discussed. By using adaptive techniques and designing a containment controller, a sufficient criterion for the system to achieve finite time synchronization is obtained. Finally, an example is given to demonstrate the validity of the theoretical results.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5;O231

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