基于随机切换的网络系统分析与控制
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摘要
信息通过共享网络交换的反馈控制系统称为网络控制系统(Networked ControlSystems，简称NCSs)。这种网络化的控制模式具有成本低、连接线数少、易于扩展维护、高效和信息资源共享等诸多优点，使得网络控制系统已在工业自动化、智能交通、机器人、航空航天、国防等领域获得了广泛的应用。然而，把网络的引入传统的反馈控制系统，也不可避免地把网络本身存在的问题带入控制系统中：如有限的通信带宽、网络传输时滞、数据丢包、多包传输、时钟异步等等。这些问题的存在，造成控制系统的控制指令往往不能够及时执行，其结果导致系统性能变差，严重的甚至会造成系统不稳定。以上问题在传统的控制系统中不存在或是可以忽略不计，因此基于传统的控制理论给出的控制设计和分析难以直接应用到网络控制系统中，迫切需要针对网络控制系统的特点发展系统分析与控制设计的新思想、新概念、新方法，研究开发适合于网络环境的控制策略。所以，对NCSs的分析与综合是当前控制理论研究的重要内容，也是国内外学者研究的热点问题之一。
本文从控制理论及算法的角度出发，围绕NCSs中存在的一些基本问题：网络诱导时滞、丢包和数据无序传输等，利用时滞系统理论、线性跳变系统理论、Lyapunov稳定性理论及线性矩阵不等式(LMIs)方法、V-K迭代算法、自由权矩阵方法和贪婪算法等方法对NCSs的建模、稳定性、容错和控制进行了相关研究，并得到针对这些基本问题的一些研究结果。
针对网络时滞问题建立了时变时滞NCSs的模型(包括确定系统和不确定系统)，然后利用时滞系统理论、锥补线性化方法和自由权矩阵方法研究了NCSs的稳定性和镇定性问题，并基于LMIs形式给出具有较小保守性的时滞相关稳定和镇定条件。
基于离散时间马尔可夫跳变线性系统理论，研究了在网络中的随机时滞、丢包和数据包无序传输随网络负载变化而改变的情况下，系统稳定性与控制器设计问题。提出一种能够根据网络负载变化而自动调节的智能随机切换控制器，使得系统在可镇定范围大大增加的同时具有较好的动态性能。
提出一种新的依概率切换的随机切换模型用于研究网络控制系统中的执行器随机故障问题。利用V-K迭代算法，设计出能够在网络中多种随机因素干扰下诱发执行器随机故障时，保持网络控制系统均方稳定的模式依赖和模式独立容错控制器，并计算出系统对执行器随机故障的最大冗余度。
针对网络控制系统的多率本质，提出一种新的多率方法用于镇定同时具有网络诱导时滞、丢包和数据包无序传输的网络控制系统。该方法可以建立一个统一的模型用于解决网络短时滞和长时滞的镇定性问题，并在转移概率矩阵已知的条件下给出系统均方稳定的充分条件。随后通过仿真实例说明在同等条件下，多率控制器比单率控制器具有更强的鲁棒性。
基于Internet测试和分析得到的数据，把网络控制系统的一般性方法与具体的Internet特点相结合，设计出一种能够同时处理网络时滞的时变部分小于一个采样周期或大于一个采样周期且有界的一致方法。最后通过仿真比较，说明相对于一般的控制器，采用该方法设计的控制器具有较强的鲁棒性和较好的控制效果。
充分考虑无线传感器网络中多检测信号传输，且各信号时滞变化规律不同的特性，建立能够较准确描述无线传感器网络特点的网络控制系统模型，并提出一种准确性与实时性兼顾的时滞相关加权均值法构建静态输出控制器，然后利用跳变线性系统理论研究了系统的均方稳定性和均方可镇定问题。最后通过仿真实例说明了基于加权均值融合技术设计的静态输出控制器的有效性。
最后对全文进行了总结，并对今后NCSs进一步的研究和发展方向进行了展望。
Feedback control systems wherein the control loops are connected with a real-time network are called networked control systems (NCSs). The primary advantages of NCSs are low cost, reduced system wiring, simple installation and maintenances, high efficiency and shared information. As a result, NCSs have been widely applied to many complicated control systems, such as industrial automation, intelligent traffic, robot, aviation and aerospace fields, airplane manufacture. However, the insertion of the communication network in feedback control loop makes the analysis and design of NCSs complicate because it introduces some problems existing in network into control systems such as limited communication band width, network-induced delay, data packets dropout, disorder of data packets and clock asynchronous. These problems lead to control signal can not be executed immediately. As a result, performances of control systems become badly or even control system become instable. Because these problems do not exist or can be ignored in traditional feedback control systems, methods of control design and analysis based on traditional control theory is hardly applied into NCSs directly. So control strategies adapting for network environment should be found based on new ideas, new methods and new conceptions. Therefore, analysis and synthesis of NCSs have become one of the most important issues in control theories reasearch, and also have received considerable attention and interest by researchers in recent years.
In the dissertation, some essential issues of NCSs are discussed from the point of view on control theory and arithmetic. Modeling, stability analysis, fault tolerant and control problems of NCSs are investigated based on time-delay system theory, jump linear system theory, Lyapunov stability theory combined with linear matrix inequalities (LMIs) techniques, V-K iterations, free weighting matrices approach and greedy algorithm. Some new results are given as to these basic problems based on analysis and synthesis of NCSs.
As to problem of time varying delay existing in NCSs, a time-varying model including certain system and uncertain system are constructed firstly, and then stability and stabilization of these systems are discussed based on time-delay system theory, cone convex optimization theory and free weighting matrices approach. Conditions of time-dependent stability and stabilization with less conservative are given in the form of linear matrix inequalities.
Based on discrete time Markov jump linear system theory, stability and controller designed are considered when time-induced delay, packet dropout and disorder of data packets exist in NCSs at the same time. An intelligent stochastic switching controller which can self-adjust adapted for different network load is proposed to stabilize NCSs. Compared normal feedback gain controller, stochastic switching controller not only has larger stability scope but better dynamic stability performances.
A new switch model switched according to probability is proposed to discuss problem of stochastic fault about actuator. Using V-K iterations, mode-dependent and mode-independent fault tolerant controller are designed under some stochastic disturbances such as stochastic actuator fault and the maximum redundancy degree of system is given.
As to the multirate essences of NCSs, a new multirate method is proposed to stabilize NCSs combined with time-induced delay, packet dropout and disorder of data packets. The advantage of this method is that, a unitized model which can describe short time delay and long time delay is constructed. Based on this unitized model, stability and stabilization of NCSs are discussed. Sufficient condition of mean square stability of NCSs is given when transition matrix is known. From simulation example we know, multirate controller has stronger robust performance compared with single controller under the same conditions.
Based on analysis of data coming from test in internet and normal method developed from general NCSs, a unitized method which can deal with time varying part of time delay less than one sampling period or more than one sampling period but bounded is proposed . Finally from simulation we know, compared normal controller, controller designed with this method has strong robust performances.
Consider the character of multi-signal transimisson and different statistic rules of every class of signal in wireless sensor network, a new model which can describe wireless sensor networked control systems accurately is constructed firstly. A static output feedback controller is designed through weighted mean method, and then stability and stabilization of wireless sensor network are disscussed using jump linear systems. Numerical examples and simulations show that the methods are effective.
Finally, a summary has been done for all discussions in the dissertation. The research works in further study are presented.
本文从控制理论及算法的角度出发，围绕NCSs中存在的一些基本问题：网络诱导时滞、丢包和数据无序传输等，利用时滞系统理论、线性跳变系统理论、Lyapunov稳定性理论及线性矩阵不等式(LMIs)方法、V-K迭代算法、自由权矩阵方法和贪婪算法等方法对NCSs的建模、稳定性、容错和控制进行了相关研究，并得到针对这些基本问题的一些研究结果。
针对网络时滞问题建立了时变时滞NCSs的模型(包括确定系统和不确定系统)，然后利用时滞系统理论、锥补线性化方法和自由权矩阵方法研究了NCSs的稳定性和镇定性问题，并基于LMIs形式给出具有较小保守性的时滞相关稳定和镇定条件。
基于离散时间马尔可夫跳变线性系统理论，研究了在网络中的随机时滞、丢包和数据包无序传输随网络负载变化而改变的情况下，系统稳定性与控制器设计问题。提出一种能够根据网络负载变化而自动调节的智能随机切换控制器，使得系统在可镇定范围大大增加的同时具有较好的动态性能。
提出一种新的依概率切换的随机切换模型用于研究网络控制系统中的执行器随机故障问题。利用V-K迭代算法，设计出能够在网络中多种随机因素干扰下诱发执行器随机故障时，保持网络控制系统均方稳定的模式依赖和模式独立容错控制器，并计算出系统对执行器随机故障的最大冗余度。
针对网络控制系统的多率本质，提出一种新的多率方法用于镇定同时具有网络诱导时滞、丢包和数据包无序传输的网络控制系统。该方法可以建立一个统一的模型用于解决网络短时滞和长时滞的镇定性问题，并在转移概率矩阵已知的条件下给出系统均方稳定的充分条件。随后通过仿真实例说明在同等条件下，多率控制器比单率控制器具有更强的鲁棒性。
基于Internet测试和分析得到的数据，把网络控制系统的一般性方法与具体的Internet特点相结合，设计出一种能够同时处理网络时滞的时变部分小于一个采样周期或大于一个采样周期且有界的一致方法。最后通过仿真比较，说明相对于一般的控制器，采用该方法设计的控制器具有较强的鲁棒性和较好的控制效果。
充分考虑无线传感器网络中多检测信号传输，且各信号时滞变化规律不同的特性，建立能够较准确描述无线传感器网络特点的网络控制系统模型，并提出一种准确性与实时性兼顾的时滞相关加权均值法构建静态输出控制器，然后利用跳变线性系统理论研究了系统的均方稳定性和均方可镇定问题。最后通过仿真实例说明了基于加权均值融合技术设计的静态输出控制器的有效性。
最后对全文进行了总结，并对今后NCSs进一步的研究和发展方向进行了展望。
Feedback control systems wherein the control loops are connected with a real-time network are called networked control systems (NCSs). The primary advantages of NCSs are low cost, reduced system wiring, simple installation and maintenances, high efficiency and shared information. As a result, NCSs have been widely applied to many complicated control systems, such as industrial automation, intelligent traffic, robot, aviation and aerospace fields, airplane manufacture. However, the insertion of the communication network in feedback control loop makes the analysis and design of NCSs complicate because it introduces some problems existing in network into control systems such as limited communication band width, network-induced delay, data packets dropout, disorder of data packets and clock asynchronous. These problems lead to control signal can not be executed immediately. As a result, performances of control systems become badly or even control system become instable. Because these problems do not exist or can be ignored in traditional feedback control systems, methods of control design and analysis based on traditional control theory is hardly applied into NCSs directly. So control strategies adapting for network environment should be found based on new ideas, new methods and new conceptions. Therefore, analysis and synthesis of NCSs have become one of the most important issues in control theories reasearch, and also have received considerable attention and interest by researchers in recent years.
In the dissertation, some essential issues of NCSs are discussed from the point of view on control theory and arithmetic. Modeling, stability analysis, fault tolerant and control problems of NCSs are investigated based on time-delay system theory, jump linear system theory, Lyapunov stability theory combined with linear matrix inequalities (LMIs) techniques, V-K iterations, free weighting matrices approach and greedy algorithm. Some new results are given as to these basic problems based on analysis and synthesis of NCSs.
As to problem of time varying delay existing in NCSs, a time-varying model including certain system and uncertain system are constructed firstly, and then stability and stabilization of these systems are discussed based on time-delay system theory, cone convex optimization theory and free weighting matrices approach. Conditions of time-dependent stability and stabilization with less conservative are given in the form of linear matrix inequalities.
Based on discrete time Markov jump linear system theory, stability and controller designed are considered when time-induced delay, packet dropout and disorder of data packets exist in NCSs at the same time. An intelligent stochastic switching controller which can self-adjust adapted for different network load is proposed to stabilize NCSs. Compared normal feedback gain controller, stochastic switching controller not only has larger stability scope but better dynamic stability performances.
A new switch model switched according to probability is proposed to discuss problem of stochastic fault about actuator. Using V-K iterations, mode-dependent and mode-independent fault tolerant controller are designed under some stochastic disturbances such as stochastic actuator fault and the maximum redundancy degree of system is given.
As to the multirate essences of NCSs, a new multirate method is proposed to stabilize NCSs combined with time-induced delay, packet dropout and disorder of data packets. The advantage of this method is that, a unitized model which can describe short time delay and long time delay is constructed. Based on this unitized model, stability and stabilization of NCSs are discussed. Sufficient condition of mean square stability of NCSs is given when transition matrix is known. From simulation example we know, multirate controller has stronger robust performance compared with single controller under the same conditions.
Based on analysis of data coming from test in internet and normal method developed from general NCSs, a unitized method which can deal with time varying part of time delay less than one sampling period or more than one sampling period but bounded is proposed . Finally from simulation we know, compared normal controller, controller designed with this method has strong robust performances.
Consider the character of multi-signal transimisson and different statistic rules of every class of signal in wireless sensor network, a new model which can describe wireless sensor networked control systems accurately is constructed firstly. A static output feedback controller is designed through weighted mean method, and then stability and stabilization of wireless sensor network are disscussed using jump linear systems. Numerical examples and simulations show that the methods are effective.
Finally, a summary has been done for all discussions in the dissertation. The research works in further study are presented.
引文
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