On Stochastic Sampling-based H_∞ Filtering For Networked Systems

Networked control systems(NCSs) are feedback systems in which the network is used as the medium to transmit information. Compared with the conventional point-to-point control systems, NCSs have numerous advantages, such as low wiring cost, convenient installation and strong expandability. At present, NCSs have been a principal research focus in both industry and academia. However, a series of issues are inevitably introduced by transmitting data with finite bandwidth resources, for instance, the network-induced delay, data-packet dropout and quantization error.For NCSs, all information needs to be sampled before being transmitted to the controller, and it has been identified that the system performance cannot be optimal by adopting the uniform sampling method. Due to the unpredictability of network, the stochastic sampling-based scheme has attracted much research attention for the NCSs analysis and design. So far some satisfactory results have been reported, however, there are still several challenging problems to be resolved. To name a few, the random binary sequence is firstly introduced by the existing methods to describe the switching process of the sampling periods, therefore it is hard to extend their conclusions to a more general case. Then, the input-delay approach is adopted in literature for the analysis of system stability, but the processing procedure is complicated, making it difficult to take overall consideration of common problems in NCSs, such as network-induced delay, data-packet dropout and quantization. What’s more, the relationship between the system performance and characteristic parameters such as packet loss ratio and quantization density has been ignored by existing researchers.On the other hand, state estimation is of great importance in designing the control system. The Kalman filter is a significant method for state estimation, but this method requires a precise mathematical model of plant and the noise input to be stationary Gaussian. However, in practical systems, uncertainties do exist. In this scenario, the Kalman filter can not achieve a desired performance. An alternative approach is the H∞ filtering technique, which has attracted much attention in the last a few decades. Based on the above discussion, the stochastic sampling-based H∞ filtering for networked systems is mainly investigated in this thesis, the specific contents are as follows:Firstly, the H∞ filtering problem is investigated for a class of networked systems with stochastic sampling, quantization and data-packet dropout. A Markov chain is introduced to describe the stochastic sampling process of sensors, and the effects caused by quantization and packet dropout are transformed into the parameter uncertainty of the filtering system. Based on the Lyapunov stability theory and stochastic analysis method, a sufficient condition is obtained such that the filtering system is stochastically stable and achieves an expected disturbance attenuation level. The design procedure for the optimal filter is also provided.Secondly, the energy-efficient H∞ filtering is investigated for wireless networked systems. Energy conservation strategies such as the stochastic sampling with non-uniform periods, the measurement size reduction scheme and the stochastic transmission protocol are introduced to reduce transmission data quantity and consequently achieve the energy reservation goal. In our work, the networked filtering system subjected to the energy consumption constraint is modelled as a Markovian switched system with uncertainties. Based on the stochastic switched system approach, sufficient conditions are obtained such that the filtering system is exponentially stable in the mean-square sense with a prescribed disturbance attenuation level, and the design method for the corresponding filter is given simultaneously.Finally, the distributed H∞ filtering problem is discussed for a class of wireless sensor networks. System measurements are collected through a sensor network stochastically and the phenomena such as random missing measurement and quantization are also considered. A distributed scheme is presented for this estimation task. Based on the Lyapunov stability theory and the stochastic system analysis method, a sufficient condition is obtained such that the augmented filtering system is stochastically stable and achieves a desired disturbance attenuation level. The design procedure of the distributed filter is also provided.The simulations of some examples are given to demonstrate the effectiveness of the proposed results. At the end of this thesis, a summary of the full thesis as well as the directions for further investigation are given.