网络环境下反馈控制系统的分析与设计
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摘要
网络控制系统具有成本低、可实现资源共享、远程操作与控制，具有较高的诊断能力、安装与维护简便、能有效减少系统的重量和体积、增加了系统的灵活性和可靠性等优点，因此被广泛应用于设备制造、工业自动化、航空航天和医疗保健等领域。然而网络的引入又带来了很多新的不确定性，如丢包、延迟等，这些都对经典控制问题提出了新的挑战。本文主要考虑网络的引入所带来的数据包丢失和网络带宽有限等问题，结合经典控制理论、矩阵分析中的相关知识和现有文献关于网络建模等，研究了网络控制系统的均方可检测性、间歇量化卡尔曼滤波、线性二次高斯控制、信息滤波以及贝叶斯Fisher信息等问题。通过仿真实验对所得结论的可行性进行了验证。
本文主要做了以下四个方面的研究：
一是研究了随机乘性信道多输出系统的均方可检测–离散情形问题。基于单包传输及多包传输的多输出网络化系统，以及乘性信道由白噪声过程描述，讨论了此种情况下的网络化系统的可检测问题。对于单个数据包传输情形，采用二分法，给出网络化系统均方可检测时用系统信道容量表示的临界值；对于多个平行数据包传输情形，在网络资源可以在所有输出通道中任意分配的假设下，给出了用系统米勒测度表示的网络化系统均方可检测的充分必要条件，同时将所得结论应用到擦除信道和有界扇形不确定信道，其结论与现有的文献一致，进而展示结论的可行性。
二是将基于乘性信道多输出系统的均方可检测问题的离散情形扩展到连续时间系统，其中输出通道的不可靠性由白噪声过程描述。出于有限的通信容量和多个信道通信系统中的网络资源分配的考虑,我们假设所定义的总体服务质量固定的,且可以在各个输出通道中任意分配。指出为确保网络连续系统均方可检测，存在一个对整个服务质量的最小要求，该最小要求用系统的不稳定度来表示。最后用擦除信道和有界扇形随机不确定信道中给出应用。
三是基于最优Lloyd-Max量化器及具有固定比特率的有损网络，讨论了间歇量化卡尔曼滤波，间歇量化信息滤波以及此种网络下线性二次高斯控制问题，并且给出了间歇量化卡尔曼滤波，间歇量化信息滤波稳定性条件，该条件可用给定的比特率和收包率来表示；同时也用信息论的角度给出稳定性条件。通过假设观测值为高斯，我们推导出此种网络下最优线性二次高斯控制及相应的最小能量函数，该控制可用两个黎卡提方程来表示，一是线性二次高斯控制，一是间歇量化卡尔曼滤波误差方差阵方程。仿真例子验证方案的有效性。
四是讨论了混合模型的卡尔曼滤波和信息滤波，以及从各种模型的接收值中获得状态的贝叶斯Fisher信息。信息滤波和卡尔曼滤波的各种优缺点都有讨论。对于高斯情形，由于协方差矩阵的逆称为贝叶斯Fisher信息，描述了观测值中所含状态信息量的多少，这种特征启发我们进一步讨论贝叶斯Fisher信息并与信息滤波作以比较。贝叶斯Fisher信息本身逆的倒数就是所有均方误差估计的下界，为我们设计估计器的时候提供一个理论下界。
Since networked control systems (NCS) ofer many advantages such as low cost,sharing of resource, remote operation and control, a high diagnostic capability, simpleinstallation and maintenance, efectively reduced the weight and volume of the system,increased system fexibility and reliability, etc., recently, they have found widely used inequipment manufacturing, industrial automation, aerospace and medical care and otherfelds. However, the introduction of the network brings a lot of new uncertainties, suchas packet loss, delay, etc., which raise new challenges to the classical control problem.In this dissertation, we focus on the problems of data packet dropout and limited net-work bandwidth which are induced by the introduction of network. Integrating classicalcontrol theory, relevant knowledge of matrix analysis and network modeling in existingliterature, we investigate the detectability, intermittent quantized Kalman fltering, linearquadratic Gaussian control and Information fltering of the NCS, etc.. The efectivenessand applicability of the theoretical results proposed are demonstrated by the simulationexamples.
This dissertation mainly includes the following four contents:
Firstly, we investigate the mean square detectability problem for multi-output net-worked discrete time systems via single packet or multiple packets transmission, wherea multiplicative white noise models the unreliability of output channels. For the singlepacket case, by adopting the bisection technique, we give the critical value (lower bound)of mean square capacity for ensuring mean square detectability. For the multi-parallelmultiple packets transmission strategy, a necessary and sufcient condition on overallmean square capacity for mean square detectability in terms of the Mahler measure ortopological entropy of the plant is presented, under the assumption that the given networkresource can be allocated among all the output channels. Applications in erasure-typechannel and channel with stochastic sector-bounded uncertainty are provided to demon-strate the results.
Secondly, we extend the mean square detectability problem to multi-output net-worked continuous time systems, where multiplicative white noise models the unreliabil-ity of output channels. Motivated by the limited communication capacity and networkresource allocation in multiple channel communication systems, we assume that the over- all quality of service defned in this paper is fxed and can be assigned among the outputchannels. We show that there exists a minimal requirement on the overall quality ofservice in terms of the instability degree of the plant for achieving the mean square de-tectability of the networked system. Applications in erasure-type channel and channelwith stochastic sector-bounded uncertainty are provided to demonstrate the results.
Thirdly, we discuss the batch intermittent quantized Kalman flter (BIQKF), Infor-mation flter (BIQIF), and LQG control over lossy digital links using dynamic Lloyd-Max quantizer. A necessary and sufcient condition is presented for the Stability of theBIQKF and the BIQIF, The condition, which is expressed in terms of the bit rate andthe arrival probability initially. Meanwhile, we further explain the stability conditionfrom the perspective of information theory. Under the assumption that the observationis approximately Gaussian, it is shown that the separation principle remains valid underthe quantized output signal which is used to be transmitted over lossy networks. Theoptimal LQG controller is then given in terms of two Riccati diference equations associ-ated respectively with the Kalman flter with intermittent quantized observations and thestandard LQR control. The corresponding minimum cost is also derived. An illustrativeexample is provided.
Fourthly, we discuss Kalman flter and information flter for mixed models, and thenderive Bayesian Fisher information of the state from the receiving value of the mixedmodels. Advantages of information flter over Kalman flter are also discussed. For aGaussian case, since inverse of the covariance matrix (also called Bayesian Fisher infor-mation) provides the measure of information about the state present in the observations,so we also study the Bayesian Fisher information which is defned as the expectation withrespect to all the random variables, namely the measurements and the systems state, andcompare them with information flter. The reciprocal of the inverse of the Bayesian Fisherinformation itself is the lower bound of the mean square error estimation, which providesa theoretical lower bound for us to design the estimator.
本文主要做了以下四个方面的研究：
一是研究了随机乘性信道多输出系统的均方可检测–离散情形问题。基于单包传输及多包传输的多输出网络化系统，以及乘性信道由白噪声过程描述，讨论了此种情况下的网络化系统的可检测问题。对于单个数据包传输情形，采用二分法，给出网络化系统均方可检测时用系统信道容量表示的临界值；对于多个平行数据包传输情形，在网络资源可以在所有输出通道中任意分配的假设下，给出了用系统米勒测度表示的网络化系统均方可检测的充分必要条件，同时将所得结论应用到擦除信道和有界扇形不确定信道，其结论与现有的文献一致，进而展示结论的可行性。
二是将基于乘性信道多输出系统的均方可检测问题的离散情形扩展到连续时间系统，其中输出通道的不可靠性由白噪声过程描述。出于有限的通信容量和多个信道通信系统中的网络资源分配的考虑,我们假设所定义的总体服务质量固定的,且可以在各个输出通道中任意分配。指出为确保网络连续系统均方可检测，存在一个对整个服务质量的最小要求，该最小要求用系统的不稳定度来表示。最后用擦除信道和有界扇形随机不确定信道中给出应用。
三是基于最优Lloyd-Max量化器及具有固定比特率的有损网络，讨论了间歇量化卡尔曼滤波，间歇量化信息滤波以及此种网络下线性二次高斯控制问题，并且给出了间歇量化卡尔曼滤波，间歇量化信息滤波稳定性条件，该条件可用给定的比特率和收包率来表示；同时也用信息论的角度给出稳定性条件。通过假设观测值为高斯，我们推导出此种网络下最优线性二次高斯控制及相应的最小能量函数，该控制可用两个黎卡提方程来表示，一是线性二次高斯控制，一是间歇量化卡尔曼滤波误差方差阵方程。仿真例子验证方案的有效性。
四是讨论了混合模型的卡尔曼滤波和信息滤波，以及从各种模型的接收值中获得状态的贝叶斯Fisher信息。信息滤波和卡尔曼滤波的各种优缺点都有讨论。对于高斯情形，由于协方差矩阵的逆称为贝叶斯Fisher信息，描述了观测值中所含状态信息量的多少，这种特征启发我们进一步讨论贝叶斯Fisher信息并与信息滤波作以比较。贝叶斯Fisher信息本身逆的倒数就是所有均方误差估计的下界，为我们设计估计器的时候提供一个理论下界。
Since networked control systems (NCS) ofer many advantages such as low cost,sharing of resource, remote operation and control, a high diagnostic capability, simpleinstallation and maintenance, efectively reduced the weight and volume of the system,increased system fexibility and reliability, etc., recently, they have found widely used inequipment manufacturing, industrial automation, aerospace and medical care and otherfelds. However, the introduction of the network brings a lot of new uncertainties, suchas packet loss, delay, etc., which raise new challenges to the classical control problem.In this dissertation, we focus on the problems of data packet dropout and limited net-work bandwidth which are induced by the introduction of network. Integrating classicalcontrol theory, relevant knowledge of matrix analysis and network modeling in existingliterature, we investigate the detectability, intermittent quantized Kalman fltering, linearquadratic Gaussian control and Information fltering of the NCS, etc.. The efectivenessand applicability of the theoretical results proposed are demonstrated by the simulationexamples.
This dissertation mainly includes the following four contents:
Firstly, we investigate the mean square detectability problem for multi-output net-worked discrete time systems via single packet or multiple packets transmission, wherea multiplicative white noise models the unreliability of output channels. For the singlepacket case, by adopting the bisection technique, we give the critical value (lower bound)of mean square capacity for ensuring mean square detectability. For the multi-parallelmultiple packets transmission strategy, a necessary and sufcient condition on overallmean square capacity for mean square detectability in terms of the Mahler measure ortopological entropy of the plant is presented, under the assumption that the given networkresource can be allocated among all the output channels. Applications in erasure-typechannel and channel with stochastic sector-bounded uncertainty are provided to demon-strate the results.
Secondly, we extend the mean square detectability problem to multi-output net-worked continuous time systems, where multiplicative white noise models the unreliabil-ity of output channels. Motivated by the limited communication capacity and networkresource allocation in multiple channel communication systems, we assume that the over- all quality of service defned in this paper is fxed and can be assigned among the outputchannels. We show that there exists a minimal requirement on the overall quality ofservice in terms of the instability degree of the plant for achieving the mean square de-tectability of the networked system. Applications in erasure-type channel and channelwith stochastic sector-bounded uncertainty are provided to demonstrate the results.
Thirdly, we discuss the batch intermittent quantized Kalman flter (BIQKF), Infor-mation flter (BIQIF), and LQG control over lossy digital links using dynamic Lloyd-Max quantizer. A necessary and sufcient condition is presented for the Stability of theBIQKF and the BIQIF, The condition, which is expressed in terms of the bit rate andthe arrival probability initially. Meanwhile, we further explain the stability conditionfrom the perspective of information theory. Under the assumption that the observationis approximately Gaussian, it is shown that the separation principle remains valid underthe quantized output signal which is used to be transmitted over lossy networks. Theoptimal LQG controller is then given in terms of two Riccati diference equations associ-ated respectively with the Kalman flter with intermittent quantized observations and thestandard LQR control. The corresponding minimum cost is also derived. An illustrativeexample is provided.
Fourthly, we discuss Kalman flter and information flter for mixed models, and thenderive Bayesian Fisher information of the state from the receiving value of the mixedmodels. Advantages of information flter over Kalman flter are also discussed. For aGaussian case, since inverse of the covariance matrix (also called Bayesian Fisher infor-mation) provides the measure of information about the state present in the observations,so we also study the Bayesian Fisher information which is defned as the expectation withrespect to all the random variables, namely the measurements and the systems state, andcompare them with information flter. The reciprocal of the inverse of the Bayesian Fisherinformation itself is the lower bound of the mean square error estimation, which providesa theoretical lower bound for us to design the estimator.
引文
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