H_∞ Filtering And Control For Stochastic Networked Control Systems

The networked control systems(NCSs) refer to a class of spatially distributed closed-loop systems where the actuators, sensors and controllers are connected by communication networks. NCSs have the advantages of simple connection, easy expansion, convenient for maintenance, and strong interaction, etc., which have been applied in many fields of national economy. But due to the limited network bandwidths, there exist random phenomena inevitable such as packet losses and time delays, and so on during the transmissions of data packets. At the same time, the introduction of the networks increases the complexity of the systems such that the systems will suffer from nonlinear disturbances caused by the environment etc. As for the above characteristics of the NCSs and in the consideration of all kinds of uncertainties during the data transmissions, we investigate the H∞ filtering and control problems in this paper for the NCSs by using Lyapunov stability theory and linear matrix inequality technique as well as stochastic control and robust control theories. The main research contents and innovations are as follows:1. For the NCSs with random packet losses and transmission delays in sensor channels and controller channels, the H∞ control problem has been studied where the two cases of one-step delays and multi-step delays are considered, respectively. For the NCSs with packet losses and one-step transmission delays, by state augmentation method, an H∞ controller is designed based on the observer of the augmented state. Sufficient conditions of exponential stability in the mean square sense are given for the closed-loop systems, and the solutions of controller parameters are presented in LMI form by using the cone complementarity linearization(CCL) iterative algorithm. For the NCSs in the presence of packet dropouts and multi-step transmission delays, an H∞ controller is designed based on a full-order state observer. By applying Lyapunov theory, a sufficient condition is given which makes the closed-loop system is mean square asymptotically stable and satisfies a specified H∞ performance. Furthermore, the solutions of controller parameters are obtained in the LMI form.2. For the uncertain NCSs in the presence of random packet losses and one-step transmission delay and in the presence of packet dropouts and multi-step transmission delays, the full-order filters with robust performance are studied. In the case of one-step delay, by introducing slack variables, a robust H∞ performance criterion is derived. The existence conditions and design approaches of the robust filters are obtained based on LMI method. In the case of multi-step bounded transmission delays, we model the NCSs by using a set of independent identically distribution Bernoulli random variables. By constructing the appropriate Lyapunov function, an H∞ filter design method is proposed which makes the filtering error system asymptotically stable in the mean square sense, and also guarantees the robustness to the uncertain parameters of the systems and disturbance inputs. The filter parameters are obtained by solving the LMI.3. For the multi-channel NCSs with random nonlinear disturbances, the H∞ filter design problem is concerned. Considering that when the observation signals of multiple sensors are transmitted through the network, the packet loss probability and time delay probability for each channel will be different, the two mutually independent random diagonal matrices are adopted to model the random one-step delay and multiple packet losses phenomena. The exponential stability in the mean square sense of the filtering error system is also analyzed. By introducing the new slack variables, the full order filter with H∞ performance is designed based on LMI technology. And compared with the traditional method of direct decomposition of Lyapunov matrix, the superiority of the design method is verified.4. For the stochastic nonlinear NCSs with data packet losses and multi-step transmission delays, the H∞ filtering problem is investigated. Considering the packet disorder caused by the network induced delay, it is possible that there will be more than one data packets and may be multiple received by the receiver at every moment. A group of Bernoulli distributed random variables is applied to model the NCSs, and all the data received at each time are described by state augmentation. Meanwhile, the nonlinear disturbances occurred randomly are dependent on the delayed state. By constructing proper Lyapunov function, a sufficient condition is obtained which makes the filtering error system is mean square asymptotically stable and satisfies a prespecified H∞ performance. Based on this condition, the filter design problem is converted into a convex optimization problem with LMI constraints and the H∞ filter design method is presented.