Research On Filtering And Control For Networked Discrete-time Systems Based On Markov Chain

Networked control systems (NCSs) possess the advantages of reducing cost, facilitating sys-tem maintenance and increasing system agility, which not only attract a number of scholars to its theoretical research, but also gain widespread applications in the industry, unmanned aerial ve-hicles, vehicular networks, traffic control and so on. Due to the fact that the shared network is employed to transmit the information, new challenges would appear in studying the stability and the performance of the closed-loop systems, such as quantization error analysis, packet dropout and transmission delay compensating and sampler design and so on.This thesis considers the problems of sampling, packet dropout, communication constraints, sensor failure and sensor nonlinearity in the NCSs. Based on the discrete-time Markov jump system analysis method and the robust control method, the main results are obtained as follows.1. For the networked output feedback control systems, in the output channel (sensor-to-controller channel) the randomly sampled measurement is modeled as a Markov chain. An event driv-en transmitter, which depends on measurement sampling period, is introduced to transmit the control signal in the input channel (controller-to-actuator channel). In order to achieve a less conservative result, a novel output feedback controller, including both sampling and event-driven transmitter induced delay indexes, is proposed. The sufficient and necessary condition of the mean-square stability, the stochastic stability and the exponentially mean-square stability for the closed-loop system is established. Then the observer and controller gains are obtained respectively. Finally, based on the Zigbee real communication channel, a numerical example is shown to demonstrate the effectiveness of the proposed method.2. For the multiple-input and multiple-output networked feedback control systems with stochas-tic parameters, the packet dropout of each output channel is modeled as an independent Markov chain. Based on the packet dropout in the output channel, the multiple-density quantizer is designed in the input channel. The conservatism of the closed-loop system is re- duced by designing the packet dropout-dependent observer gains, and the quantizer density-dependent controller gains. A sufficient condition of the exponential mean-square stability for the closed-loop system is established and the controller gains as well as the observer gains are designed.3. For the multiple-input and multiple-output networked feedback control systems with com-munication constraints, the Conventional Round-Robin Scheduling (CRRS) with simple structure, and the Dynamic Round-Robin Scheduling (DRRS), which guarantees the con-trollability and the detectability of the resultant systems are applied. For the unreliable com-munication channels, two independent homogeneous Markov chains are selected to model the packet dropouts phenomenon in the output channels and the input channels, respectively. An auxiliary system with augmented Markov chain is established by the lifting technique. The necessary and sufficient conditions of the exponentially mean-square stability for the closed-loop system with two different scheduling methods are obtained.4. For the multiple output networked uncertain systems, the phenomena of randomly occurring sensor nonlinearities and packet dropouts are considered, which are represented by multiple independent three states Markov chains with partially unknown transition probabilities. A one to one mapping is constructed to map the multiple independent Markov chains to an augmented one for facilitating the resultant system analysis. A sufficient condition of the exponentially mean-square stability with H∞performance is obtained for the filtering error systems, and the parameters of the full-order filter is obtained.5. For the networked fuzzy systems with sensor failure, multiple-failure models are established. The Markov chain is applied to describe the switching conditions among the failure models, since the sensor failure model cannot be directly obtained, the transition probability depen-dent asynchronous filters are designed. By constructing the fuzzy set dependent Lyapunov function, a less conservative sufficient condition, which guarantees the filtering error systems to be exponentially mean-square stable and dissipative, is derived, and the parameters of the full-order filter is obtained.