基于Markov链的网络化离散系统滤波与控制研究
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摘要
网络化系统具有成本低、易于安装与维护、系统柔性好的优点,在过去的二十年里不仅在理论研究方面吸引了学者,在工业领域、无人机及智能交通等实际应用领域也得到了很大的推广。由于网络共享的特点,给闭环系统的稳定性和性能分析带来了新的挑战,如量化误差的分析、数据丢包与传输时滞的补偿和采样器的设计等问题。
本论文针对网络化控制系统中的采样、丢包、通信受限、传感器故障及传感器非线性问题,采用离散Markov跳变系统分析方法和鲁棒控制方法,通过研究取得了以下主要成果。
1.针对网络化输出反馈控制系统,输出通道(传感器到控制器的通道)端,用Markov链描述了随机采样测量序列,输入通道(控制器到执行器的通道)端,采用了基于采样周期的事件驱动传输策略。通过设计采样诱导时滞和事件驱动诱导时滞双依赖的输出反馈控制器,有效地降低了系统的保守性。得到了闭环系统满足均方稳定、随机稳定和指数均方稳定的充分必要条件,并给出了相应控制器和观测器的增益。基于ZigBee搭建的无线传输网络和数值例子验证了算法的有效性。
2.针对多输入和多输出网络化随机参数反馈控制系统,采用独立的Markov链描述了每个输出通道的丢包情况,基于丢包情况在输入通道中设计了多密度量化器。通过设计丢包依赖的观测器增益和量化密度依赖的控制器增益,有效地降低了系统的保守性。给出了闭环系统满足指数均方稳定的充分条件,并给出了相应控制器和观测器的增益。
3.针对通道容量受限的多输入和多输出反馈控制系统,设计了结构简单的静态调度和保证调度传输系统能控和能观的动态调度策略以减少网络资源的使用率。采样两个独立的Markov链描述了输入和输出通道的丢包情况。基于基于扩维技术,通过构造均方意义下等价的扩维Markov辅助系统,分别给出了两种不同调度情况下系统满足指数均方稳定的充要条件。
4.针对多输出网络化不确定系统,考虑了传感器随机非线性和网络随机丢包现象。采用三维部分转移概率未知的Markov链描述滤波器收到的测量值情况。通过构造一一映射把多个独立的Markov链转换成一个高维的Markov链。给出了滤波误差系统满足指数均方稳定和H∞性能的充分条件,并给出了相应全阶滤波器的参数。
5.针对传感器存在故障的网络化模糊系统,建立了多模态故障模型。并用Markov链描述不同故障之间的切换关系。由于故障模态不可直接获得,设计了概率依赖的异构耗散滤波器。通过构建模糊集依赖的Lyapunov函数,给出了滤波误差系统满足指数均方稳定和耗散性的低保守性充分条件,并给出了相应全阶滤波器的参数。
Networked control systems (NCSs) possess the advantages of reducing cost, facilitating sys-tem maintenance and increasing system agility, which not only attract a number of scholars to its theoretical research, but also gain widespread applications in the industry, unmanned aerial ve-hicles, vehicular networks, traffic control and so on. Due to the fact that the shared network is employed to transmit the information, new challenges would appear in studying the stability and the performance of the closed-loop systems, such as quantization error analysis, packet dropout and transmission delay compensating and sampler design and so on.
This thesis considers the problems of sampling, packet dropout, communication constraints, sensor failure and sensor nonlinearity in the NCSs. Based on the discrete-time Markov jump system analysis method and the robust control method, the main results are obtained as follows.
1. For the networked output feedback control systems, in the output channel (sensor-to-controller channel) the randomly sampled measurement is modeled as a Markov chain. An event driv-en transmitter, which depends on measurement sampling period, is introduced to transmit the control signal in the input channel (controller-to-actuator channel). In order to achieve a less conservative result, a novel output feedback controller, including both sampling and event-driven transmitter induced delay indexes, is proposed. The sufficient and necessary condition of the mean-square stability, the stochastic stability and the exponentially mean-square stability for the closed-loop system is established. Then the observer and controller gains are obtained respectively. Finally, based on the Zigbee real communication channel, a numerical example is shown to demonstrate the effectiveness of the proposed method.
2. For the multiple-input and multiple-output networked feedback control systems with stochas-tic parameters, the packet dropout of each output channel is modeled as an independent Markov chain. Based on the packet dropout in the output channel, the multiple-density quantizer is designed in the input channel. The conservatism of the closed-loop system is re- duced by designing the packet dropout-dependent observer gains, and the quantizer density-dependent controller gains. A sufficient condition of the exponential mean-square stability for the closed-loop system is established and the controller gains as well as the observer gains are designed.
3. For the multiple-input and multiple-output networked feedback control systems with com-munication constraints, the Conventional Round-Robin Scheduling (CRRS) with simple structure, and the Dynamic Round-Robin Scheduling (DRRS), which guarantees the con-trollability and the detectability of the resultant systems are applied. For the unreliable com-munication channels, two independent homogeneous Markov chains are selected to model the packet dropouts phenomenon in the output channels and the input channels, respectively. An auxiliary system with augmented Markov chain is established by the lifting technique. The necessary and sufficient conditions of the exponentially mean-square stability for the closed-loop system with two different scheduling methods are obtained.
4. For the multiple output networked uncertain systems, the phenomena of randomly occurring sensor nonlinearities and packet dropouts are considered, which are represented by multiple independent three states Markov chains with partially unknown transition probabilities. A one to one mapping is constructed to map the multiple independent Markov chains to an augmented one for facilitating the resultant system analysis. A sufficient condition of the exponentially mean-square stability with H∞performance is obtained for the filtering error systems, and the parameters of the full-order filter is obtained.
5. For the networked fuzzy systems with sensor failure, multiple-failure models are established. The Markov chain is applied to describe the switching conditions among the failure models, since the sensor failure model cannot be directly obtained, the transition probability depen-dent asynchronous filters are designed. By constructing the fuzzy set dependent Lyapunov function, a less conservative sufficient condition, which guarantees the filtering error systems to be exponentially mean-square stable and dissipative, is derived, and the parameters of the full-order filter is obtained.
本论文针对网络化控制系统中的采样、丢包、通信受限、传感器故障及传感器非线性问题,采用离散Markov跳变系统分析方法和鲁棒控制方法,通过研究取得了以下主要成果。
1.针对网络化输出反馈控制系统,输出通道(传感器到控制器的通道)端,用Markov链描述了随机采样测量序列,输入通道(控制器到执行器的通道)端,采用了基于采样周期的事件驱动传输策略。通过设计采样诱导时滞和事件驱动诱导时滞双依赖的输出反馈控制器,有效地降低了系统的保守性。得到了闭环系统满足均方稳定、随机稳定和指数均方稳定的充分必要条件,并给出了相应控制器和观测器的增益。基于ZigBee搭建的无线传输网络和数值例子验证了算法的有效性。
2.针对多输入和多输出网络化随机参数反馈控制系统,采用独立的Markov链描述了每个输出通道的丢包情况,基于丢包情况在输入通道中设计了多密度量化器。通过设计丢包依赖的观测器增益和量化密度依赖的控制器增益,有效地降低了系统的保守性。给出了闭环系统满足指数均方稳定的充分条件,并给出了相应控制器和观测器的增益。
3.针对通道容量受限的多输入和多输出反馈控制系统,设计了结构简单的静态调度和保证调度传输系统能控和能观的动态调度策略以减少网络资源的使用率。采样两个独立的Markov链描述了输入和输出通道的丢包情况。基于基于扩维技术,通过构造均方意义下等价的扩维Markov辅助系统,分别给出了两种不同调度情况下系统满足指数均方稳定的充要条件。
4.针对多输出网络化不确定系统,考虑了传感器随机非线性和网络随机丢包现象。采用三维部分转移概率未知的Markov链描述滤波器收到的测量值情况。通过构造一一映射把多个独立的Markov链转换成一个高维的Markov链。给出了滤波误差系统满足指数均方稳定和H∞性能的充分条件,并给出了相应全阶滤波器的参数。
5.针对传感器存在故障的网络化模糊系统,建立了多模态故障模型。并用Markov链描述不同故障之间的切换关系。由于故障模态不可直接获得,设计了概率依赖的异构耗散滤波器。通过构建模糊集依赖的Lyapunov函数,给出了滤波误差系统满足指数均方稳定和耗散性的低保守性充分条件,并给出了相应全阶滤波器的参数。
Networked control systems (NCSs) possess the advantages of reducing cost, facilitating sys-tem maintenance and increasing system agility, which not only attract a number of scholars to its theoretical research, but also gain widespread applications in the industry, unmanned aerial ve-hicles, vehicular networks, traffic control and so on. Due to the fact that the shared network is employed to transmit the information, new challenges would appear in studying the stability and the performance of the closed-loop systems, such as quantization error analysis, packet dropout and transmission delay compensating and sampler design and so on.
This thesis considers the problems of sampling, packet dropout, communication constraints, sensor failure and sensor nonlinearity in the NCSs. Based on the discrete-time Markov jump system analysis method and the robust control method, the main results are obtained as follows.
1. For the networked output feedback control systems, in the output channel (sensor-to-controller channel) the randomly sampled measurement is modeled as a Markov chain. An event driv-en transmitter, which depends on measurement sampling period, is introduced to transmit the control signal in the input channel (controller-to-actuator channel). In order to achieve a less conservative result, a novel output feedback controller, including both sampling and event-driven transmitter induced delay indexes, is proposed. The sufficient and necessary condition of the mean-square stability, the stochastic stability and the exponentially mean-square stability for the closed-loop system is established. Then the observer and controller gains are obtained respectively. Finally, based on the Zigbee real communication channel, a numerical example is shown to demonstrate the effectiveness of the proposed method.
2. For the multiple-input and multiple-output networked feedback control systems with stochas-tic parameters, the packet dropout of each output channel is modeled as an independent Markov chain. Based on the packet dropout in the output channel, the multiple-density quantizer is designed in the input channel. The conservatism of the closed-loop system is re- duced by designing the packet dropout-dependent observer gains, and the quantizer density-dependent controller gains. A sufficient condition of the exponential mean-square stability for the closed-loop system is established and the controller gains as well as the observer gains are designed.
3. For the multiple-input and multiple-output networked feedback control systems with com-munication constraints, the Conventional Round-Robin Scheduling (CRRS) with simple structure, and the Dynamic Round-Robin Scheduling (DRRS), which guarantees the con-trollability and the detectability of the resultant systems are applied. For the unreliable com-munication channels, two independent homogeneous Markov chains are selected to model the packet dropouts phenomenon in the output channels and the input channels, respectively. An auxiliary system with augmented Markov chain is established by the lifting technique. The necessary and sufficient conditions of the exponentially mean-square stability for the closed-loop system with two different scheduling methods are obtained.
4. For the multiple output networked uncertain systems, the phenomena of randomly occurring sensor nonlinearities and packet dropouts are considered, which are represented by multiple independent three states Markov chains with partially unknown transition probabilities. A one to one mapping is constructed to map the multiple independent Markov chains to an augmented one for facilitating the resultant system analysis. A sufficient condition of the exponentially mean-square stability with H∞performance is obtained for the filtering error systems, and the parameters of the full-order filter is obtained.
5. For the networked fuzzy systems with sensor failure, multiple-failure models are established. The Markov chain is applied to describe the switching conditions among the failure models, since the sensor failure model cannot be directly obtained, the transition probability depen-dent asynchronous filters are designed. By constructing the fuzzy set dependent Lyapunov function, a less conservative sufficient condition, which guarantees the filtering error systems to be exponentially mean-square stable and dissipative, is derived, and the parameters of the full-order filter is obtained.
引文
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