Research On Networked Control Systems With Quantization

With the rapid development of sensing,computing,and communication technologies,the research on networked control systems has attracted much attention.Quantization is one of the key features in networked control systems,which will significantly degrade the performance and even damage the stability of the systems.In this dissertation,we study the effect of quantization on the estimation and control performance of networked control systems for a linear timeinvariant discrete-time stochastic plant,when the measurements are encoded and then transmitted via a noiseless digital channel.The main contributions of this dissertation can be concluded as:1)Optimum design of real-time predictive encoding systems.In terms of the dynamic characteristics of the linear system,we adopt a dynamic Lloyd-Max quantization scheme and design the corresponding optimal real-time predictive encoder.The minimum conditional mean-square error distortion of the measurement is also obtained.For the decoder,two recursive algorithms for the minimum mean-square error estimator of the state of the system are presented.One is exact,while the other one is approximate.With the Gaussian fit assumption,the optimality of the dynamic Lloyd-Max quantization scheme is proved.Furthermore,the joint optimality of the encoder and the decoder is also proved.An upper bound for the ensemble average performance is presented.2)State estimation with quantized measurements.To avoid the difficulties caused by nonlinearity in quantization laws and the high computational cost,a sub-optimal algorithm is proposed.A sequence of upper bounds of state estimation error covariances is obtained in terms of a difference Riccati equation.It is found that the upper bound of the estimation error covariance is convergent if and only if the averaged quantization data rate is greater than a critical value which is determined by poles of the system and certain design parameters in the state estimator.3)Posterior Cramér-Rao lower bound for state estimation with quantized measurements.With the use of a real-time differential coded system whose quantizer is designed for a Gaussian pdf,the posterior Cramér-Rao lower bound is obtained in terms of the model of the system and the mean-square distortion of the real-time differential coded system.The proposed posterior Cramér-Rao lower bound allows us to understand the state estimation performance degradation due to quantization.A lower bound of the posterior Cramér-Rao lower bound,which is a modified algebraic Riccati equation,is derived,and the minimum data rate necessary for the convergence of the posterior Cramér-Rao lower bound is presented in terms of the unstable eigenvalues of the system.4)Linear quadratic Gaussian control with quantized measurements.For the optimal encoder,the optimal controller,which is a certainty equivalence controller,is obtained by constructing a special networked control system.For the certainty equivalence controller,the optimal encoder is discussed.In order to obtain the trade-off relation between the data rate and the control performance of networked control systems,the infinite-horizon linear quadratic Gaussian control performance is studied,and the minimum data rate necessary for the convergence of the control performance is presented in terms of the unstable eigenvalues of the system.