网络控制系统的分析与综合
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摘要
网络控制系统(NCSs)是指通过一个实时网络构成的闭环控制系统。与传统的点对点的控制系统相比，网络控制系统具有成本低，资源共享，易于安装和维护等优点。然而由于网络的引入，也给网络控制系统带来了许多挑战性的问题，像时间延迟、数据丢包、多包传输等都给网络控制系统的分析与设计带来了比较大的困难。
本文利用线性矩阵不等式方法和李雅普诺夫稳定性理论，对存在数据丢包、时间延迟、通讯限制、变采样周期等因素影响的网络控制系统进行了研究。主要内容分为以下几方面：
1.对变采样周期的网络控制系统的量化状态反馈控制问题进行了研究。通过构造一个新的包括时变采样周期和量化信号的网络控制系统的模型，使用李雅普诺夫稳定性理论和线性矩阵不等式方法，给出了一类具有变采样周期的网络控制系统的量化状态反馈控制器的设计方法，并证明了在该控制器作用下，闭环系统是随机指数稳定的。
2.对变采样周期非线性网络控制系统进行了分析和控制。首先对一类具有随机时延和控制器增益扰动的非线性网络控制系统的非脆弱保性能控制问题进行了研究。基于变采样周期的方法，将网络控制系统建模为非线性的Markov跳变系统，利用Lyapunov方法设计的非脆弱状态反馈控制器保证闭环系统是随机渐近稳定的并且它的性能函数值不超过一个规定的上界。然后对一类具有随机时延和非线性扰动的网络控制系统的鲁棒随机稳定化问题进行了研究，利用变采样周期的方法，把连续被控对象离散化，将网络控制系统建模为部分转移概率未知的非线性Markov跳变系统。利用随机Lyapunov稳定性理论方法证明了闭环系统的随机稳定性，同时也得到了非线性扰动项的最大界。
3.对变采样周期网络控制系统的模型预测控制问题进行了研究。利用变采样周期的方法，将连续的被控对象离散化，从而建模为部分转移概率未知的Markov跳变系统。首先针对一类具有随机时延和输入约束的网络控制系统,通过线性矩阵不等式的方法给出了保证整个闭环系统随机渐近稳定且滚动时域性能指标在线最小化的充分条件和预测状态反馈控制器的设计方法。然后针对一类具有随机时延和外部扰动的网络控制系统，基于min-max性能指标的在线方法设计了H预测状态反馈控制器。
4.研究了具有通讯限制的网络控制系统的分析与控制问题。首先研究了具有有限通讯信道和时变时延的网络控制系统的控制问题。提出了一种新的具有有限通讯信道和时变时延的离散时间网络控制系统的模型。通过选取适当的Lyapunov函数，并利用离散的Jenson不等式设计了状态反馈控制器。然后对存在有限通讯信道和不确定随机时延的离散非线性网络控制系统的稳定性问题进行了研究。提出了一种新的同时考虑有限通讯信道和随机时延的控制率模型。通过构造新的随机Lyapunov函数,给出了保证闭环系统随机稳定，同时又能最大化非线性界的一个充分条件。
5.研究了一类具有随机时延和随机丢包的非线性网络控制系统的动态输出反馈控制问题。首先将随机时延和随机丢包建模为两个相互独立的随机变量，然后通过设计基于观测器的动态输出反馈控制器给出了闭环系统随机稳定的充分条件，通过求解一组线性矩阵不等式给出了丢包率、转移概率矩阵和非线性界之间的关系。
Networked control systems(NCSs) are feedback control loops closed through a realtime network. Compared with conventional point-to-point control systems, NCSs havemany attractive advantages, such as low cost, resource sharing, simple installation，andeasy maintenance and so on. On the other hand, the introduction of networks alsopresents some challenging problem such as quantization, packet dropout andmultiple-packet transmission and so on, which bring difficulties for analysis and designof NCSs.
In this dissertation, In terms of the Lyapunov approach and linear matrixinequality(LMI) techniques, the research of NCSs with network-induced delay, packeddropout, communication constraint, and variable-period sampling are studied. The maincontents are as follows:
1. The quantized state feedback control problem for a class of networked controlsystem under variable-period sampling is studied. A new model with time-varyingsampling period and quantization signal is presented. By Lyapunov stability theory andlinear matrix inequality techniques, a quantized state feedback controller is designed fora class of networked control system under variable-period sampling, under the action ofthe controller, the closed loop system is exponentially mean-square stabilization.
2. Analysis and control for a class of nonlinear networked control systems undervariable-period is addressed. Firstly, the problem of non-fragile guaranteed cost controlfor a class of nonlinear networked control systems with random delay and controllergain disturbance is considered. Based on variable-period sampling approach, thenetworked control systems are modeled as a nonlinear Markov jump systems. Under theaction of the non-fragile state feedback controller which is designed by means of theLyapunov method, the closed-loop system is stochastic asymptotically stable and itscost function value less than the specified upper bound. Secondly, the problem of robuststabilization for a class of networked control systems with random delay and nonlinearperturbation is considered. Applying variable-period sampling method, thediscretization of networked control systems is modeled as a nonlinear Markovian jumpsystems with partly unknown transition probabilities. The stochastic stability of theclosed-loop system is proved via Lyapunov stability theory, and at the same timemaximizes the bound on the non-linearity.
3. The problem of model predictive control is proposed for networked control systems under variable-period sampling. Applying variable-period sampling method,the networked control systems is discretized and modeled as a Markovian jump linearsystems with partly unknown transition probabilities. Firstly, for a class of networkedcontrol systems with random delay and input constraints, using the linear matrixinequality method, the sufficient conditions are presented to guarantee asymptoticalstability and an upper bound of the receding horizon performance index of the closedloop system, and the design method of the predictive controller is also derived.Secondly, for a class of networked control systems with random delay and disturbances,the H predictive controller is designed based on the online method based on themin-max performance index.
4. Analysis and control for a class of networked control systems with limitedcommunication channels is addressed. Firstly, the problem of control for a class ofnetworked control systems with limited communication channels and time-varyingdelay is considered. A new model is proposed to describe the discrete-time networkedcontrol systems with both limited communication channels and time-varying delay. Bychoosing appropriate Lyapunov function, the state feedback controller is designed byusing the discrete Jenson ineauality. Secondly, the problem of the stabilization for aclass of nonlinear networked control systems with limited communication channels anduncertain random delay is investigated. A novel control law model is proposed to takethe limited communication channels and uncertain random delay into considerationsimultaneously. By constructing the new stochastic Lyapunov function, a sufficientcondition is presented which guarantees the stochastic stability of the closed-loopsystems and at the same time maximizes the nonlinear bound.
5. The problem of dynamic output feedback control is investigated for a class ofnonlinear networked control systems with both random packet dropout and randomdelay. Random packet dropout and random delay are modeled as two independentrandom variables. An observer-based dynamic output feedback controller is designed. Asufficient condition is presented for the stochastic stabilization of the closed systems.The quantitative relationship between the dropout rate, transition probability matrix andnonlinear level is derived by solving a set of linear matrix inequalities.
本文利用线性矩阵不等式方法和李雅普诺夫稳定性理论，对存在数据丢包、时间延迟、通讯限制、变采样周期等因素影响的网络控制系统进行了研究。主要内容分为以下几方面：
1.对变采样周期的网络控制系统的量化状态反馈控制问题进行了研究。通过构造一个新的包括时变采样周期和量化信号的网络控制系统的模型，使用李雅普诺夫稳定性理论和线性矩阵不等式方法，给出了一类具有变采样周期的网络控制系统的量化状态反馈控制器的设计方法，并证明了在该控制器作用下，闭环系统是随机指数稳定的。
2.对变采样周期非线性网络控制系统进行了分析和控制。首先对一类具有随机时延和控制器增益扰动的非线性网络控制系统的非脆弱保性能控制问题进行了研究。基于变采样周期的方法，将网络控制系统建模为非线性的Markov跳变系统，利用Lyapunov方法设计的非脆弱状态反馈控制器保证闭环系统是随机渐近稳定的并且它的性能函数值不超过一个规定的上界。然后对一类具有随机时延和非线性扰动的网络控制系统的鲁棒随机稳定化问题进行了研究，利用变采样周期的方法，把连续被控对象离散化，将网络控制系统建模为部分转移概率未知的非线性Markov跳变系统。利用随机Lyapunov稳定性理论方法证明了闭环系统的随机稳定性，同时也得到了非线性扰动项的最大界。
3.对变采样周期网络控制系统的模型预测控制问题进行了研究。利用变采样周期的方法，将连续的被控对象离散化，从而建模为部分转移概率未知的Markov跳变系统。首先针对一类具有随机时延和输入约束的网络控制系统,通过线性矩阵不等式的方法给出了保证整个闭环系统随机渐近稳定且滚动时域性能指标在线最小化的充分条件和预测状态反馈控制器的设计方法。然后针对一类具有随机时延和外部扰动的网络控制系统，基于min-max性能指标的在线方法设计了H预测状态反馈控制器。
4.研究了具有通讯限制的网络控制系统的分析与控制问题。首先研究了具有有限通讯信道和时变时延的网络控制系统的控制问题。提出了一种新的具有有限通讯信道和时变时延的离散时间网络控制系统的模型。通过选取适当的Lyapunov函数，并利用离散的Jenson不等式设计了状态反馈控制器。然后对存在有限通讯信道和不确定随机时延的离散非线性网络控制系统的稳定性问题进行了研究。提出了一种新的同时考虑有限通讯信道和随机时延的控制率模型。通过构造新的随机Lyapunov函数,给出了保证闭环系统随机稳定，同时又能最大化非线性界的一个充分条件。
5.研究了一类具有随机时延和随机丢包的非线性网络控制系统的动态输出反馈控制问题。首先将随机时延和随机丢包建模为两个相互独立的随机变量，然后通过设计基于观测器的动态输出反馈控制器给出了闭环系统随机稳定的充分条件，通过求解一组线性矩阵不等式给出了丢包率、转移概率矩阵和非线性界之间的关系。
Networked control systems(NCSs) are feedback control loops closed through a realtime network. Compared with conventional point-to-point control systems, NCSs havemany attractive advantages, such as low cost, resource sharing, simple installation，andeasy maintenance and so on. On the other hand, the introduction of networks alsopresents some challenging problem such as quantization, packet dropout andmultiple-packet transmission and so on, which bring difficulties for analysis and designof NCSs.
In this dissertation, In terms of the Lyapunov approach and linear matrixinequality(LMI) techniques, the research of NCSs with network-induced delay, packeddropout, communication constraint, and variable-period sampling are studied. The maincontents are as follows:
1. The quantized state feedback control problem for a class of networked controlsystem under variable-period sampling is studied. A new model with time-varyingsampling period and quantization signal is presented. By Lyapunov stability theory andlinear matrix inequality techniques, a quantized state feedback controller is designed fora class of networked control system under variable-period sampling, under the action ofthe controller, the closed loop system is exponentially mean-square stabilization.
2. Analysis and control for a class of nonlinear networked control systems undervariable-period is addressed. Firstly, the problem of non-fragile guaranteed cost controlfor a class of nonlinear networked control systems with random delay and controllergain disturbance is considered. Based on variable-period sampling approach, thenetworked control systems are modeled as a nonlinear Markov jump systems. Under theaction of the non-fragile state feedback controller which is designed by means of theLyapunov method, the closed-loop system is stochastic asymptotically stable and itscost function value less than the specified upper bound. Secondly, the problem of robuststabilization for a class of networked control systems with random delay and nonlinearperturbation is considered. Applying variable-period sampling method, thediscretization of networked control systems is modeled as a nonlinear Markovian jumpsystems with partly unknown transition probabilities. The stochastic stability of theclosed-loop system is proved via Lyapunov stability theory, and at the same timemaximizes the bound on the non-linearity.
3. The problem of model predictive control is proposed for networked control systems under variable-period sampling. Applying variable-period sampling method,the networked control systems is discretized and modeled as a Markovian jump linearsystems with partly unknown transition probabilities. Firstly, for a class of networkedcontrol systems with random delay and input constraints, using the linear matrixinequality method, the sufficient conditions are presented to guarantee asymptoticalstability and an upper bound of the receding horizon performance index of the closedloop system, and the design method of the predictive controller is also derived.Secondly, for a class of networked control systems with random delay and disturbances,the H predictive controller is designed based on the online method based on themin-max performance index.
4. Analysis and control for a class of networked control systems with limitedcommunication channels is addressed. Firstly, the problem of control for a class ofnetworked control systems with limited communication channels and time-varyingdelay is considered. A new model is proposed to describe the discrete-time networkedcontrol systems with both limited communication channels and time-varying delay. Bychoosing appropriate Lyapunov function, the state feedback controller is designed byusing the discrete Jenson ineauality. Secondly, the problem of the stabilization for aclass of nonlinear networked control systems with limited communication channels anduncertain random delay is investigated. A novel control law model is proposed to takethe limited communication channels and uncertain random delay into considerationsimultaneously. By constructing the new stochastic Lyapunov function, a sufficientcondition is presented which guarantees the stochastic stability of the closed-loopsystems and at the same time maximizes the nonlinear bound.
5. The problem of dynamic output feedback control is investigated for a class ofnonlinear networked control systems with both random packet dropout and randomdelay. Random packet dropout and random delay are modeled as two independentrandom variables. An observer-based dynamic output feedback controller is designed. Asufficient condition is presented for the stochastic stabilization of the closed systems.The quantitative relationship between the dropout rate, transition probability matrix andnonlinear level is derived by solving a set of linear matrix inequalities.
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