具有时延和丢包的鲁棒网络控制系统研究
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摘要
随着计算机通信网络技术的发展,将通信网络应用到存在大量传感器、控制器和执行器的复杂控制系统中,已经成为控制系统的一个发展趋势。这种通过通信网络形成闭环的反馈控制系统称为网络控制系统。与传统的控制系统相比,网络控制系统具有连线少、占用空间少、实现成本低、安装维护方便、灵活性高、能够实现远程控制等优点,已经被广泛应用于现代制造企业、汽车、航天器以及远程操作等诸多领域。然而,网络控制系统回路中引入的通信网络也产生了网络诱导时延和数据包丢失等问题,同时对于实际的控制系统而言,要建立被控对象精确的数学模型是十分困难的。为了使网络控制系统对被控对象模型不确定性和外界干扰等具有较小的敏感性,许多学者进行了鲁棒网络控制系统的研究,取得了很多成果,但是仍然存在一些问题有待于解决。为此,本文主要进行了如下几方面的研究:
1.针对具有随机时变网络诱导时延和异步数据包丢失的网络控制系统的镇定问题,将随机网络诱导时延表示成恒定的平均时延与不确定时延之和,网络诱导时延的不确定性可化为系统状态方程系数矩阵的不确定性,用具有两个事件速率约束的异步动态系统来描述具有随机时变网络诱导时延和异步数据包丢失的网络控制系统,根据异步动态系统理论,分别给出了状态反馈网络控制系统和动态输出反馈网络控制系统指数稳定的充分条件,通过给定的充分条件可以求出保证网络控制系统指数稳定的状态反馈控制器和动态输出反馈控制器。
2.针对具有随机时变网络诱导时延和马尔可夫链丢包网络控制系统容易受到外部干扰的问题,根据马尔可夫跳变系统理论,将网络控制系统建模为一个具有两个模式的马尔可夫跳变线性系统,给出了基于线性矩阵不等式形式的状态反馈网络控制系统鲁棒H_∞控制器存在的充分条件;当网络控制系统中的被控对象的状态很难或不能测量时,以线性矩阵不等式的形式给出了动态输出反馈网络控制系统鲁棒H_∞控制器存在的充分条件,所设计的控制器不仅能使网络控制系统鲁棒随机稳定而且能将外部扰动抑制在给定的水平。
3.针对网络控制系统中被控对象具有参数不确定性时,系统的线性二次型最优控制很难实现的问题,研究了具有随机时变网络诱导时延和马尔可夫链丢包的网络控制系统的保性能控制,利用马尔可夫跳变系统理论,将网络控制系统建模为具有两个模式的马尔可夫跳变线性系统,以线性矩阵不等式的形式给出了不仅能使网络控制系统随机稳定而且使系统性能指标不超过一个上界的保性能控制器存在的充分条件。
4.针对网络控制系统中传感数据和控制数据分装在多个数据包进行传输时,各个数据包的网络诱导时延不相同的问题,在分析被控对象与控制器的输入输出关系的基础上,将多包传输的网络控制系统建模为具有多个时延的系统,通过在Lyapunov泛函中考虑网络诱导时延上界之间的关系以及估计Lyapunov泛函导数上界的时候不忽略有用信息的方法,得到了多包传输网络控制系统新的延迟依赖稳定性条件,与已有的结果相比,所提出的稳定性条件具有较小的保守性。
With the development of communication network technology, there is an increasing tendency to apply communication network to control systems where a lot of sensors, controllers and actuators exist. The control systems wherein control loops are closed through communication network are called networked control systems. Compared with the traditional control systems, networked control systems have advantages of less wire and volume, low implementation cost, easy maintenance, high flexibility and easy tele-operation and so on. So networked control systems can be observed in many areas such as modern manufacturing plants, cars, aerial vehicles, tele-operation etc. But, the communication network in the control loop brings about the problems of network-induced delay and packet dropout. It is difficult to model the controlled plant exactly in real systems. Many scholars have researched robust control of networked systems in order to make networked control systems less sensitive to the uncertainty and external disturbance. However, there still exist some problems to be solved. The following problems are studied in this dissertation:
1. The stabilization of networked control systems with random network-induced delay and asynchronous packet dropout is considered. The network-induced delay is divided into the constant average delay and the uncertain delay and transformed into the coefficients uncertainty of state space equation. Networked control systems are modeled as asynchronous dynamical systems with two events constraints. According to the theory of asynchronous dynamical systems, the stabilization of networked control systems is studied. The sufficient conditions of exponential stability of state feedback and dynamical output feedback networked control systems are given respectively. The controllers can be obtained by the conditions.
2. The networked controlled plant is often disturbed. The robust H_∞control of networked control systems with random network-induced delay and packet dropout governed by Markov chain is studied. The networked control systems are modeled as markovian jump linear systems with two modes. The sufficient condition of state feedback robust H_∞controller is given in terms of linear matrix inequalities. When the states of the plant are difficult to measure, the sufficient condition of output feedback robust H_∞controller is presented based on linear matrix inequalities. The designed controllers can stabilize the networked control systems and attenuate the disturbance to a prescribed level.
3. When the controlled plant is a system with parametric uncertainties, the linear quadratic optimal control is difficult to implement. The guaranteed cost control of networked control systems with random network-induced delay and packet dropout governed by Markov chain is addressed. The networked control systems are modeled as markovian jump linear systems with two modes. The sufficient condition of guaranteed cost controller is given in terms of linear matrix inequalities. The guaranteed cost controller makes not only the networked control systems stochastic stability but also the performance index less than an upper bound.
4. When the sensor data and control data of networked control systems are lumped into multiple packets to transmit, the network-induced delays of the packets are different from each other. Based on the relationship between the outputs and inputs of the plant and the controller, the networked control systems with multiple packets transmission are modeled as system with multiple delays. A new delay dependent stability condition of networked control systems is obtained by taking the relationship between the delay upper bounds into account in Lyapunov functional and estimating the upper bound of the derivative of Lyapunov functional without ignoring the additional useful terms. Compared with the existing results, the proposed condition is less conservative.
1.针对具有随机时变网络诱导时延和异步数据包丢失的网络控制系统的镇定问题,将随机网络诱导时延表示成恒定的平均时延与不确定时延之和,网络诱导时延的不确定性可化为系统状态方程系数矩阵的不确定性,用具有两个事件速率约束的异步动态系统来描述具有随机时变网络诱导时延和异步数据包丢失的网络控制系统,根据异步动态系统理论,分别给出了状态反馈网络控制系统和动态输出反馈网络控制系统指数稳定的充分条件,通过给定的充分条件可以求出保证网络控制系统指数稳定的状态反馈控制器和动态输出反馈控制器。
2.针对具有随机时变网络诱导时延和马尔可夫链丢包网络控制系统容易受到外部干扰的问题,根据马尔可夫跳变系统理论,将网络控制系统建模为一个具有两个模式的马尔可夫跳变线性系统,给出了基于线性矩阵不等式形式的状态反馈网络控制系统鲁棒H_∞控制器存在的充分条件;当网络控制系统中的被控对象的状态很难或不能测量时,以线性矩阵不等式的形式给出了动态输出反馈网络控制系统鲁棒H_∞控制器存在的充分条件,所设计的控制器不仅能使网络控制系统鲁棒随机稳定而且能将外部扰动抑制在给定的水平。
3.针对网络控制系统中被控对象具有参数不确定性时,系统的线性二次型最优控制很难实现的问题,研究了具有随机时变网络诱导时延和马尔可夫链丢包的网络控制系统的保性能控制,利用马尔可夫跳变系统理论,将网络控制系统建模为具有两个模式的马尔可夫跳变线性系统,以线性矩阵不等式的形式给出了不仅能使网络控制系统随机稳定而且使系统性能指标不超过一个上界的保性能控制器存在的充分条件。
4.针对网络控制系统中传感数据和控制数据分装在多个数据包进行传输时,各个数据包的网络诱导时延不相同的问题,在分析被控对象与控制器的输入输出关系的基础上,将多包传输的网络控制系统建模为具有多个时延的系统,通过在Lyapunov泛函中考虑网络诱导时延上界之间的关系以及估计Lyapunov泛函导数上界的时候不忽略有用信息的方法,得到了多包传输网络控制系统新的延迟依赖稳定性条件,与已有的结果相比,所提出的稳定性条件具有较小的保守性。
With the development of communication network technology, there is an increasing tendency to apply communication network to control systems where a lot of sensors, controllers and actuators exist. The control systems wherein control loops are closed through communication network are called networked control systems. Compared with the traditional control systems, networked control systems have advantages of less wire and volume, low implementation cost, easy maintenance, high flexibility and easy tele-operation and so on. So networked control systems can be observed in many areas such as modern manufacturing plants, cars, aerial vehicles, tele-operation etc. But, the communication network in the control loop brings about the problems of network-induced delay and packet dropout. It is difficult to model the controlled plant exactly in real systems. Many scholars have researched robust control of networked systems in order to make networked control systems less sensitive to the uncertainty and external disturbance. However, there still exist some problems to be solved. The following problems are studied in this dissertation:
1. The stabilization of networked control systems with random network-induced delay and asynchronous packet dropout is considered. The network-induced delay is divided into the constant average delay and the uncertain delay and transformed into the coefficients uncertainty of state space equation. Networked control systems are modeled as asynchronous dynamical systems with two events constraints. According to the theory of asynchronous dynamical systems, the stabilization of networked control systems is studied. The sufficient conditions of exponential stability of state feedback and dynamical output feedback networked control systems are given respectively. The controllers can be obtained by the conditions.
2. The networked controlled plant is often disturbed. The robust H_∞control of networked control systems with random network-induced delay and packet dropout governed by Markov chain is studied. The networked control systems are modeled as markovian jump linear systems with two modes. The sufficient condition of state feedback robust H_∞controller is given in terms of linear matrix inequalities. When the states of the plant are difficult to measure, the sufficient condition of output feedback robust H_∞controller is presented based on linear matrix inequalities. The designed controllers can stabilize the networked control systems and attenuate the disturbance to a prescribed level.
3. When the controlled plant is a system with parametric uncertainties, the linear quadratic optimal control is difficult to implement. The guaranteed cost control of networked control systems with random network-induced delay and packet dropout governed by Markov chain is addressed. The networked control systems are modeled as markovian jump linear systems with two modes. The sufficient condition of guaranteed cost controller is given in terms of linear matrix inequalities. The guaranteed cost controller makes not only the networked control systems stochastic stability but also the performance index less than an upper bound.
4. When the sensor data and control data of networked control systems are lumped into multiple packets to transmit, the network-induced delays of the packets are different from each other. Based on the relationship between the outputs and inputs of the plant and the controller, the networked control systems with multiple packets transmission are modeled as system with multiple delays. A new delay dependent stability condition of networked control systems is obtained by taking the relationship between the delay upper bounds into account in Lyapunov functional and estimating the upper bound of the derivative of Lyapunov functional without ignoring the additional useful terms. Compared with the existing results, the proposed condition is less conservative.
引文
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