基于隐马尔可夫模型的网络化控制系统建模与控制
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摘要
网络化控制系统是一种通过实时通信网络进行数据交换的分布式反馈控制系统。与传统的点对点控制系统相比,网络化控制系统具有减少系统布线、易于系统扩展和维护、增强系统灵活性和可靠性等优点。然而,由于网络带宽是有限的,导致数据在网络传输过程中不可避免地存在网络诱导时延。而且,由于受到网络负荷、节点竞争、网络堵塞等诸多表征网络状态的随机因素的影响,网络时延往往呈现出随机变化的特征。网络时延是导致网络化控制系统性能下降甚至不稳定的主要原因,寻找有效的网络时延建模方法在网络化控制系统建模与控制研究中占有重要地位。在这一背景下,本论文从网络时延受控于网络状态这一时延产生机理出发,引入离散时间隐马尔可夫模型对网络时延进行建模研究,并在此基础上研究仅存在前向网络短时延的网络化控制系统的建模与控制问题。具体内容包含以下几个方面:
1.建立网络时延的离散时间隐马尔可夫模型,并在此基础上实现对当前采样周期内前向网络时延的预测。首先,分别采用平均量化法和K-均值聚类量化法对网络时延进行量化处理。然后,用网络状态构成隐含的马尔可夫链过程,用时延量化序列构成可见的观察过程,建立网络时延的离散时间隐马尔可夫模型,并采用不完全数据期望最大化算法对离散时间隐马尔可夫模型进行训练,得到模型参数的最优估计。最后,利用Viterbi算法估计与时延序列相对应的网络状态序列,并与离散时间隐马尔可夫模型参数相结合预测出当前采样周期内的前向网络时延。在平均量化下选择时延所在子区间的中点作为时延预测值,而在K-均值聚类量化下选择时延所在类的聚类中心作为时延预测值。
2.基于网络时延的离散时间隐马尔可夫模型设计网络化控制系统的状态反馈控制器,补偿了网络时延对系统性能的影响。首先,根据网络状态的马尔可夫特性将网络化控制系统建模成一个典型的离散时间马尔可夫跳变线性系统。然后,借助马尔可夫跳变线性系统的随机稳定性理论得到网络化控制系统随机稳定的充分条件,并在受控对象状态完全反馈的情况下利用该充分条件设计状态反馈控制器。进一步利用Schur补引理将状态反馈控制器的设计问题转换成线性矩阵不等式的求解问题。由于状态反馈控制器的设计过程考虑了当前采样周期内前向网络时延的预测值,所以直接补偿了时延对系统性能的影响。最后,通过仿真实验验证了所设状态反馈控制器的有效性。
3.在给定性能指标下,基于网络时延的离散时间隐马尔可夫模型设计网络化控制系统的最优控制器,获得了比状态反馈控制器更好的时延补偿效果。首先,将当前采样周期的受控对象状态和前一采样周期的控制律合并定义成一个增广状态,从而将网络化控制系统建模成一个增广状态系统模型。然后,基于贝尔曼动态规划原理设计系统在给定性能指标下的最优控制器,并且研究系统在该控制器下的指数均方稳定性问题。由于最优控制器的设计过程考虑了当前采样周期内前向网络时延的预测值,所以直接补偿了时延对系统性能的影响,而且补偿效果优于状态反馈控制器。最后,通过仿真实验验证了所设最优控制器的有效性和优越性。
4.利用TrueTime1.5工具箱为网络化控制系统设计Matlab/Simulink环境下的仿真平台:NCS-SP。使用TrueTime1.5中的Kernel模块设计NCS-SP中的传感器、控制器、执行器和干扰节点,使用TrueTime1.5中的Network模块设计控制器到执行器之间的网络,使用Simulink中的State-Space模块设计受控对象阻尼复摆。在NCS-SP上验证了本论文关于网络时延的建模和预测算法以及用来补偿时延对系统影响的系统建模与控制器设计方法,并且通过对比实验验证了K-均值聚类量化法相对于平均量化法的优越性以及最优控制器相对于状态反馈控制器的优越性。
A networked control system (NCS) is a distributed feedback control system whose data is exchanged via a real-time communication network. Compared with conventional point-to-point control systems, the NCS has enormous advantages including reduced system wiring, simplified system expansion and maintenance, and improved system flexibility and reliability. However, due to the limited network bandwidth, there are inevitably network-induced delays when the data is transmitted in the network. Moreover, the delays are random since they are governed by many stochastic factors (e.g., network load, nodes competition, network congestion). All these factors can be collected to be defined as the network states which reflect the network status and determine the randomness of delays. In the NCS, the delays degrade the system performance and even cause the system instability. So, the studies of modeling methods for the delays are critical issues in the NCS. Under such a background, this thesis introduces the discrete-time hidden Markov model (DTHMM) to model the network delays, which is based on the mechanism that the network delays are governed by the network states. Furthermore, the modeling and control methods for the NCS with short delays in the forward network (denoted as forward delays) are studied. The main contents are as follows:
1. Network-induced delays are modeled as a discrete-time hidden Markov model (DTHMM), and the forward delay in the current sampling period is predicted based on the DTHMM. First, the delays are quantized by using the uniform quantization method and the K-means clustering quantization method respectively. Then, the delays are modeled as a DTHMM, where the hidden Markov chain consists of the network states and the visible observation process consists of the quantized sequence of delays. The missing-data expectation maximization algorithm is used to train the DTHMM and derive the optimal estimation of the DTHMM parameters. Finally, the Viterbi algorithm is used to estimate the network state sequence corresponding to the quantized sequence of delays. Based on the estimated network state sequence and the derived DTHMM parameters, the forward delay in the current sampling period is predicted. Under the method of uniform quantization, the prediction is taken from the midpoint of the subinterval in which the forward delay falls, while under the method of K-means clustering quantization, the prediction is taken from the centroid of the cluster to which the forward delay belongs.
2. Based on the DTHMM delay model, a state-feedback controller is designed to compensate for the effect of the delays on the NCS. First, the NCS is modeled as a typical discrete-time Markovian jump linear system (MJLS) according to the Markovian characteristics of the network states. Then, the sufficient conditions for the stochastic stability of the NCS are obtained by using the stochastic stability theory in the MJLS, and the state-feedback controller for the NCS with full state feedback is designed based on these sufficient conditions. Furthermore, the controller design problem is solved via the linear matrix inequality approach by using the Schur complement lemma. Since the prediction of the forward delay in the current sampling period is considered in the controller design, the effect of the delay on the NCS is compensated directly. Finally, simulation experiments are done to verify the validity of the state-feedback controller.
3. Under some certain performance criteria, an optimal controller is designed for the NCS based on the DTHMM delay model. The effect of the delay on the NCS is better compensated by the optimal controller than by the state-feedback controller. First, the NCS is modeled as an augmented state system, where the augmented state consists of the plant state in the current sampling period and the control law in the previous sampling period. Then, the optimal controller under certain performance criteria is designed based on Bellman's dynamic programming principle. The optimal controller guarantees the exponential mean square stability of the NCS. Since the prediction of the forward delay in the current sampling period is considered in the optimal controller design, the effect of the delay on the NCS is compensated directly. Compared with the state-feedback controller, the optimal controller renders the NCS better performance. Finally, simulation experiments are done to verify the validity and superiority of the optimal controller.
4. Based on TrueTime 1.5, a simulation platform named NCS-SP is designed for the NCS to work in Matlab/Simulink environment. The kernel block of TrueTime 1.5 is used to design the network nodes (e.g., sensor, controller, actuator, interference unit) on the NCS-SP. The network block of TrueTime 1.5 is used to design the network between the controller and the actuator on the NCS-SP. The state-space block of Simulink is used to design the plant (i.e. damped compound pendulum). The modeling and predictive methods for the network delays and the modeling and control methods for the NCS given in this thesis are all validated on the NCS-SP. Moreover, some contrastive simulation experiments are done to demonstrate the superiority of the K-means clustering quantization to the uniform quantization and the superiority of the optimal controller to the state-feedback controller.
1.建立网络时延的离散时间隐马尔可夫模型,并在此基础上实现对当前采样周期内前向网络时延的预测。首先,分别采用平均量化法和K-均值聚类量化法对网络时延进行量化处理。然后,用网络状态构成隐含的马尔可夫链过程,用时延量化序列构成可见的观察过程,建立网络时延的离散时间隐马尔可夫模型,并采用不完全数据期望最大化算法对离散时间隐马尔可夫模型进行训练,得到模型参数的最优估计。最后,利用Viterbi算法估计与时延序列相对应的网络状态序列,并与离散时间隐马尔可夫模型参数相结合预测出当前采样周期内的前向网络时延。在平均量化下选择时延所在子区间的中点作为时延预测值,而在K-均值聚类量化下选择时延所在类的聚类中心作为时延预测值。
2.基于网络时延的离散时间隐马尔可夫模型设计网络化控制系统的状态反馈控制器,补偿了网络时延对系统性能的影响。首先,根据网络状态的马尔可夫特性将网络化控制系统建模成一个典型的离散时间马尔可夫跳变线性系统。然后,借助马尔可夫跳变线性系统的随机稳定性理论得到网络化控制系统随机稳定的充分条件,并在受控对象状态完全反馈的情况下利用该充分条件设计状态反馈控制器。进一步利用Schur补引理将状态反馈控制器的设计问题转换成线性矩阵不等式的求解问题。由于状态反馈控制器的设计过程考虑了当前采样周期内前向网络时延的预测值,所以直接补偿了时延对系统性能的影响。最后,通过仿真实验验证了所设状态反馈控制器的有效性。
3.在给定性能指标下,基于网络时延的离散时间隐马尔可夫模型设计网络化控制系统的最优控制器,获得了比状态反馈控制器更好的时延补偿效果。首先,将当前采样周期的受控对象状态和前一采样周期的控制律合并定义成一个增广状态,从而将网络化控制系统建模成一个增广状态系统模型。然后,基于贝尔曼动态规划原理设计系统在给定性能指标下的最优控制器,并且研究系统在该控制器下的指数均方稳定性问题。由于最优控制器的设计过程考虑了当前采样周期内前向网络时延的预测值,所以直接补偿了时延对系统性能的影响,而且补偿效果优于状态反馈控制器。最后,通过仿真实验验证了所设最优控制器的有效性和优越性。
4.利用TrueTime1.5工具箱为网络化控制系统设计Matlab/Simulink环境下的仿真平台:NCS-SP。使用TrueTime1.5中的Kernel模块设计NCS-SP中的传感器、控制器、执行器和干扰节点,使用TrueTime1.5中的Network模块设计控制器到执行器之间的网络,使用Simulink中的State-Space模块设计受控对象阻尼复摆。在NCS-SP上验证了本论文关于网络时延的建模和预测算法以及用来补偿时延对系统影响的系统建模与控制器设计方法,并且通过对比实验验证了K-均值聚类量化法相对于平均量化法的优越性以及最优控制器相对于状态反馈控制器的优越性。
A networked control system (NCS) is a distributed feedback control system whose data is exchanged via a real-time communication network. Compared with conventional point-to-point control systems, the NCS has enormous advantages including reduced system wiring, simplified system expansion and maintenance, and improved system flexibility and reliability. However, due to the limited network bandwidth, there are inevitably network-induced delays when the data is transmitted in the network. Moreover, the delays are random since they are governed by many stochastic factors (e.g., network load, nodes competition, network congestion). All these factors can be collected to be defined as the network states which reflect the network status and determine the randomness of delays. In the NCS, the delays degrade the system performance and even cause the system instability. So, the studies of modeling methods for the delays are critical issues in the NCS. Under such a background, this thesis introduces the discrete-time hidden Markov model (DTHMM) to model the network delays, which is based on the mechanism that the network delays are governed by the network states. Furthermore, the modeling and control methods for the NCS with short delays in the forward network (denoted as forward delays) are studied. The main contents are as follows:
1. Network-induced delays are modeled as a discrete-time hidden Markov model (DTHMM), and the forward delay in the current sampling period is predicted based on the DTHMM. First, the delays are quantized by using the uniform quantization method and the K-means clustering quantization method respectively. Then, the delays are modeled as a DTHMM, where the hidden Markov chain consists of the network states and the visible observation process consists of the quantized sequence of delays. The missing-data expectation maximization algorithm is used to train the DTHMM and derive the optimal estimation of the DTHMM parameters. Finally, the Viterbi algorithm is used to estimate the network state sequence corresponding to the quantized sequence of delays. Based on the estimated network state sequence and the derived DTHMM parameters, the forward delay in the current sampling period is predicted. Under the method of uniform quantization, the prediction is taken from the midpoint of the subinterval in which the forward delay falls, while under the method of K-means clustering quantization, the prediction is taken from the centroid of the cluster to which the forward delay belongs.
2. Based on the DTHMM delay model, a state-feedback controller is designed to compensate for the effect of the delays on the NCS. First, the NCS is modeled as a typical discrete-time Markovian jump linear system (MJLS) according to the Markovian characteristics of the network states. Then, the sufficient conditions for the stochastic stability of the NCS are obtained by using the stochastic stability theory in the MJLS, and the state-feedback controller for the NCS with full state feedback is designed based on these sufficient conditions. Furthermore, the controller design problem is solved via the linear matrix inequality approach by using the Schur complement lemma. Since the prediction of the forward delay in the current sampling period is considered in the controller design, the effect of the delay on the NCS is compensated directly. Finally, simulation experiments are done to verify the validity of the state-feedback controller.
3. Under some certain performance criteria, an optimal controller is designed for the NCS based on the DTHMM delay model. The effect of the delay on the NCS is better compensated by the optimal controller than by the state-feedback controller. First, the NCS is modeled as an augmented state system, where the augmented state consists of the plant state in the current sampling period and the control law in the previous sampling period. Then, the optimal controller under certain performance criteria is designed based on Bellman's dynamic programming principle. The optimal controller guarantees the exponential mean square stability of the NCS. Since the prediction of the forward delay in the current sampling period is considered in the optimal controller design, the effect of the delay on the NCS is compensated directly. Compared with the state-feedback controller, the optimal controller renders the NCS better performance. Finally, simulation experiments are done to verify the validity and superiority of the optimal controller.
4. Based on TrueTime 1.5, a simulation platform named NCS-SP is designed for the NCS to work in Matlab/Simulink environment. The kernel block of TrueTime 1.5 is used to design the network nodes (e.g., sensor, controller, actuator, interference unit) on the NCS-SP. The network block of TrueTime 1.5 is used to design the network between the controller and the actuator on the NCS-SP. The state-space block of Simulink is used to design the plant (i.e. damped compound pendulum). The modeling and predictive methods for the network delays and the modeling and control methods for the NCS given in this thesis are all validated on the NCS-SP. Moreover, some contrastive simulation experiments are done to demonstrate the superiority of the K-means clustering quantization to the uniform quantization and the superiority of the optimal controller to the state-feedback controller.
引文
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