基于模糊控制的时滞分布参数系统部分同步.docVIP

基于模糊控制的时滞分布参数系统部分同步 摘要：在此文中，基于Galerkin方法和模糊控制讨论了一类具有时滞的分布参数的部分同步问 题。首先，基于Galerkin方法分别将主系统和从系统建模简化为能反应其动力学行为的低阶常 微分方程。进而基于模型简化后的低阶常微分方程设计模糊控制器使得主从分布参数系统达到 部分同步，同时进一步给出了当主从系统达到部分同步的时候其同步误差是有界的。最后我们 通过数值仿真验证了控制器设计方法的有效性。 关键词：时滞分布参数系统;部分同步；Galerkin方法；模糊控制；线性矩阵不等式 O231.2 Partial synchronization of the distributed parameter system with time delay via fuzzy control YUAN Kun1, FEI Shu-Min2, CAO Jin-De3 1 2 School of Automation, Southeast University, Nanjing 210096 School of Automation, Southeast University, Nanjing 210096 3 Department of Mathematics, Southeast University, Nanjing 210096 Abstract: In this paper, partial synchronization of the distributed parameter system (DPS) with time delay is considered via the Galerkin’s method and the fuzzy control. First, based on the Galerkin’s method, the dynamics of master DPs and slave DPS can be described by low-order ordinary di?erential equations (ODE), respectively. Then the low-order functional ODEs is used as the basis for the design of the fuzzy controller to ensure the synchronization between the two low-order ODEs, moreover, when the slow system of master DPS and the slow system of slave DPS is synchronized, the error between master DPS and slave DPS is bounded. Some criteria are derived for stabilization and linear matrix inequality (LMI) design approach is developed. The e?ectiveness of the proposed controller design methodology is ?nally demonstrated through numerical simulation . -1- Key words: Distributed parameter system; Partial synchronization; Galerkin’s method; Fuzzy control; Linear matrix inequality. 0  Introduction Mathematically, the distributed parameter system (DPS) is usually described by partial di?erential equations (PDEs) with mixed or homogeneous boundary conditions. The main characteristic of DPS is that the outputs, the inputs, the process of states and the parameters may vary temporally as well as spatially. Such characteristic of the DPS model is di?cult to control due to its complex