一类时延网络系统鲁棒稳定性分析
发布时间：2018-09-08 09:15
【摘要】：网络系统作为一个巨大的闭环控制系统,是由许多模块化的小型闭环控制系统组成的,并通过大量的传感器、控制器和执行器等节点连接起来.网络系统中的数据包通过信道数据流量传输到不同节点,以实现远程控制.当网络繁忙时,节点中的数据包不能实现有效传送,从而会造成网络时延、网络堵塞、数据丢失等现象.基于此,控制理论界的学者提出网络控制系统的方法,有效解决了上述问题.本文基于改进型的Wirtinger不等式、Lyapunov控制理论,讨论了一类网络控制系统的鲁棒稳定性问题,并设计了许多不同性能的控制器.主要研究内容如下:1.讨论了一类简单时延网络系统的稳定性,并建立了闭环系统模型.根据Lyapunov稳定性第二方法构造函数,并保证其未知矩阵正定.将所构造的函数沿系统方向求导,通过限定时延范围、增加控制参数,并结合时滞分割法、改进型的Wirtinger不等式法对系统进行放缩,从而得到闭环系统的渐进稳定的判据,计算结果采用LMI形式表示.最后通过算例验证了所提方法的可行性.2.讨论了一类不确定时延网络系统的稳定性,并设计了闭环系统状态反馈镇定器.在满足上面条件下增加不确定性项,依照Lyapunov稳定性第二方法构造函数,并保证其未知矩阵正定.将所构造的函数沿系统方向求导,通过限定时延范围、增加控制参数,并结合时滞分割法、Schur引理、结合积分不等式、改进型的Wirtinger不等式法对系统进行放缩,从而得到不确定时延网络系统的渐进稳定的判据,并设计了闭环系统状态反馈镇定器.计算结果采用LMI形式表示.最后通过算例验证了所提方法的可行性.3.针对了一类网络闭环系统的鲁棒保性能控制器存在性的问题,设计了鲁棒保性能控制器.首先,给出鲁棒保性能控制器的定义.接着,根据Lyapunov稳定性第二方法构造函数,并保证其未知矩阵正定.将所构造的函数沿系统方向求导,通过限定时延范围,并结合时滞分割法、改进型的Wirtinger不等式法对系统进行放缩,从而得到确定时延网络系统鲁棒保性能控制器存在判据.运用相同方法对不确定性的网络闭环系统的性能进行研究,结合积分不等式和Schur引理,从而得到不确定时延网络系统鲁棒保性能控制器存在判据,并设计了鲁棒保性能控制器.计算结果采用LMI形式表示.最后通过算例验证了所提方法的可行性.4.针对了一类不确定网络系统的外部抗干扰控制器存在性的问题,设计了鲁棒H?控制器.首先,给出扰动抑制不等式的定义.接着,根据Lyapunov稳定性第二方法构造函数,并保证其未知矩阵正定.将所构造的函数沿系统方向求导,通过限定时延范围,并结合时滞分割法、Schur引理、结合积分不等式、改进型的Wirtinger不等式法对系统进行放缩,从而得到不确定时延网络系统鲁棒H?控制器存在判据,并设计了闭环系统鲁棒H?控制器.计算结果采用LMI形式表示.最后通过算例验证了所提方法的可行性.
[Abstract]:As a huge closed-loop control system, the network system is composed of many small modular closed-loop control systems connected by a large number of sensors, controllers and actuators. Data packets in the network system are transmitted to different nodes through the channel data flow to achieve remote control. When the network is busy, the section In this paper, based on the improved Wirtinger inequality and Lyapunov control theory, a class of networked control systems is discussed. The main research contents are as follows: 1. The stability of a class of simple delay network systems is discussed and the closed-loop system model is established. According to the second method of Lyapunov stability, the function is constructed and its unknown matrix is guaranteed to be positive definite. By limiting the time delay range, increasing the control parameters and combining with the time delay splitting method, the improved Wirtinger inequality method is used to scale the closed-loop system to obtain the criterion of asymptotic stability. The results are expressed in the form of LMI. Finally, the feasibility of the proposed method is verified by an example. 2. A class of uncertain time-delay network is discussed. A state feedback stabilizer for closed-loop systems is designed. The uncertainties are added to satisfy the above conditions, and the function is constructed according to the Lyapunov stability second method, and the unknown matrix is guaranteed to be positive definite. By using Schur's lemma and integral inequality, the improved Wirtinger inequality method is used to scale the system. The criterion for asymptotic stability of uncertain network systems with time-delay is obtained. A closed-loop state feedback stabilizer is designed. The results are expressed in the form of LMI. Finally, the feasibility of the proposed method is verified by an example. In this paper, the existence of robust guaranteed cost controllers for a class of network closed-loop systems is considered, and robust guaranteed cost controllers are designed. Firstly, the definition of robust guaranteed cost controllers is given. The existence criterion of robust guaranteed cost controllers for networked systems with time-delay is obtained by scaling the system with time-delay partitioning method and the improved Wirtinger inequality method. The results are expressed in the form of LMI. Finally, the feasibility of the proposed method is verified by an example. 4. A robust H? Controller is designed to solve the problem of the existence of an external anti-jamming controller for a class of uncertain network systems. Then, according to the second method of Lyapunov stability, the function is constructed and the unknown matrix is guaranteed to be positive definite. The function is derived along the direction of the system, and the system is scaled down by defining the time delay range, combining with the time delay partition method, Schur lemma, integral inequality and the improved Wirtinger inequality method. The existence criterion of robust H? Controllers for uncertain network systems with time-delay is obtained and the closed-loop robust H? Controllers are designed. The results are expressed in the form of LMI.
【学位授予单位】：广西师范学院
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP273
本文编号：2230095
[Abstract]:As a huge closed-loop control system, the network system is composed of many small modular closed-loop control systems connected by a large number of sensors, controllers and actuators. Data packets in the network system are transmitted to different nodes through the channel data flow to achieve remote control. When the network is busy, the section In this paper, based on the improved Wirtinger inequality and Lyapunov control theory, a class of networked control systems is discussed. The main research contents are as follows: 1. The stability of a class of simple delay network systems is discussed and the closed-loop system model is established. According to the second method of Lyapunov stability, the function is constructed and its unknown matrix is guaranteed to be positive definite. By limiting the time delay range, increasing the control parameters and combining with the time delay splitting method, the improved Wirtinger inequality method is used to scale the closed-loop system to obtain the criterion of asymptotic stability. The results are expressed in the form of LMI. Finally, the feasibility of the proposed method is verified by an example. 2. A class of uncertain time-delay network is discussed. A state feedback stabilizer for closed-loop systems is designed. The uncertainties are added to satisfy the above conditions, and the function is constructed according to the Lyapunov stability second method, and the unknown matrix is guaranteed to be positive definite. By using Schur's lemma and integral inequality, the improved Wirtinger inequality method is used to scale the system. The criterion for asymptotic stability of uncertain network systems with time-delay is obtained. A closed-loop state feedback stabilizer is designed. The results are expressed in the form of LMI. Finally, the feasibility of the proposed method is verified by an example. In this paper, the existence of robust guaranteed cost controllers for a class of network closed-loop systems is considered, and robust guaranteed cost controllers are designed. Firstly, the definition of robust guaranteed cost controllers is given. The existence criterion of robust guaranteed cost controllers for networked systems with time-delay is obtained by scaling the system with time-delay partitioning method and the improved Wirtinger inequality method. The results are expressed in the form of LMI. Finally, the feasibility of the proposed method is verified by an example. 4. A robust H? Controller is designed to solve the problem of the existence of an external anti-jamming controller for a class of uncertain network systems. Then, according to the second method of Lyapunov stability, the function is constructed and the unknown matrix is guaranteed to be positive definite. The function is derived along the direction of the system, and the system is scaled down by defining the time delay range, combining with the time delay partition method, Schur lemma, integral inequality and the improved Wirtinger inequality method. The existence criterion of robust H? Controllers for uncertain network systems with time-delay is obtained and the closed-loop robust H? Controllers are designed. The results are expressed in the form of LMI.
【学位授予单位】：广西师范学院
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP273
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