【作者】 陈明；

【导师】 李威；

【作者基本信息】 北京化工大学 ， 应用数学， 2009， 硕士

【摘要】 开关到达系统作为一种典型的混合系统,会产生混沌现象。为抑制其混沌现象,相继产生设定缓冲器值的上限或下限方法、设定服务器连续注入时间上限方法、可控内部连通方法、时滞脉冲反馈控制方法等。时滞脉冲反馈控制是时滞反馈控制与脉冲控制的结合与改进,本文将该方法的控制范围扩展到每个边界来控制混沌(多边控制),分析了单边控制与多边控制的收敛性。接着假定开关时间大于0时,开关到达系统会产生损失情况。对该方法控制时间的选择加以修改,确保其不仅能控制混沌现象,还能降低系统损失率。主要结论与方法如下:1、介绍开关到达系统,引入庞加莱截面来定义系统中不稳定周期轨,列举和对比针对该系统混沌现象的经典控制方法。2、对开关到达系统实施多边控制(如N=3):提出控制方法;阐述控制时间的选择以及控制具体实施过程;数值验证控制目标为2-周期轨、3-周期轨时,该方法的控制效果,并且探测到其它周期轨的具体位置;分析该方法收敛性;证明控制系数矩阵K的存在性。3、引入渐进收敛速度和迭代矩阵谱半径概念来分析单边与多边控制收敛性,讨论迭代矩阵谱半径与控制效果之间的关系。数值检验单边与多边控制的效果。4、假定开关时间大于0时,系统会产生损失的情况。通过比较开关频率大小后,确定1-周期轨为控制目标。对控制时间加以改变来避免开关事件在实施控制时发生。数值验证不同情况下,有无实施多边控制效果的对比。更多还原

【Abstract】 Switched arrival system is used as a kind of typical hybrid system, which can lead to chaotic behavior. In order to control its chaotic behavior, many methods are proposed in succession, such as upper and lower limits placed on the volumes of the buffers, changing the limited continuous processing time, controlled internal connections and delayed impulsive feedback control. Delayed impulsive feedback control is synthesis improvement of impulsive control and time-delayed feedback control. Chaos is controlled by implementing control at each boundary (multi-sided control) in this paper. Convergence of one-sided and multi-sided control methods is also analyzed. Then under the assumption of switched time being more than zero, switched arrival system leads to loss of production. Selection of control time is changed such that chaos is not just controlled, but also loss rate of the system is decreased. The main results and methods are as follows:1 Switched arrival system is introduced. Poincare section is selected for defining unstable periodic orbits. The typical methods of chaos control are introduced. 2 Multi-sided control method is implemented in switched arrival system (such as N = 3). Control method is proposed; Selection of control time and implementation of control method are described; When control target are period-2 orbit and period-3 orbit, the effectiveness of method is numerically examined, and periodic orbits with other period are also detected. Convergence of the method is analyzed; Existence of control coefficient matrix K is proved.3 Asymptotical convergence rate and spectral radius of iterative matrix are introduced to analyze convergence of one-sided control and multi-sided control. Relation between spectral radius of iterative matrix and effectiveness of the method is discussed. One-sided control and multi-sided control are numerically examined.4 Under the assumption of switched time being more than zero, switched arrival system leads to loss of production. By comparing switched frequency, period-1 orbit is selected as control target. Control time is changed to avoid occurrence of switched event in the process of control. Loss rate of the system with or without implementing multi-sided control are compared.更多还原