论文标题
2D Kuramoto-Sivashinsky方程的采样数据控制
Sampled-data control of 2D Kuramoto-Sivashinsky equation
论文作者
论文摘要
本文介绍了矩形域上2D Kuramoto-Sivashinsky方程的采样数据控制。我们建议将2D矩形分为N子域，其中传感器提供通过通信网络传输到控制器的空间平均或点状态测量值。请注意，与2D热方程式不同，在这里我们通过点测量下的采样数据控制来管理。我们设计了通过在空间特征函数中分布的区域稳定控制器。足够的条件确保了闭环系统的区域稳定性，以线性基质不平等（LMI）的形式建立。通过求解这些LMI，我们发现了对最初条件集的估计值，从该条件开始，系统的状态轨迹将指数收敛至零。数值示例证明了结果的效率。
This paper addresses sampled-data control of 2D Kuramoto-Sivashinsky equation over a rectangular domain. We suggest to divide the 2D rectangular into N sub-domains, where sensors provide spatially averaged or point state measurements to be transmitted through communication network to the controller. Note that differently from 2D heat equation, here we manage with sampled-data control under point measurements. We design a regionally stabilizing controller applied through distributed in space characteristic functions. Sufficient conditions ensuring regional stability of the closed-loop system are established in terms of linear matrix inequalities (LMIs). By solving these LMIs, we find an estimate on the set of initial conditions starting from which the state trajectories of the system are exponentially converging to zero. A numerical example demonstrates the efficiency of the results.
