Analysis And Designs For Feedback Control Systems Under Network Circumstance

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.