Research On Stabilization And Optimal Design Of Networked Control Systems

In networked control systems (NCSs), the control loops are connected with a real-time network. Compared with the conventional control systems whose components are connected via point-to-point cables, the primary advantages of NCSs are reduced wiring, low cost, simple installation and maintenances and shared information. As a result, NCSs have been widely applied to many complicated control systems, such as industry, traffic, military and medical treatment. Networks bring convenience to control systems, at the same time, it bring new challenging issues, such as network-induced delays, packet losses, and signal quantization. These are all potential causes for the performace deterioration or even the instability of NCSs. Thus, traditional control theories and analysis methods must be reevaluated before they can be applied to NCSs. Considering the combination effects of several network issues, this dissertation studies the stabilization and optimal design of NCSs. The main contents of this dissertation are outlined as follows.The stabilization problem for a basic wireless networked control system with packet loss is studied. Utilising the relation between packet loss probability and signal-to-noise power ratio (SNR) of the wireless channel, the wireless link model is simplified as a Bernoulli process. Moreover, the WNCS can be expressed as a Markov jump linear system. The necessary and sufficient condition of mean-square stability for the WNCS is established for given packet loss probability. The stabilisation condition is developed for the existence of a stabilising state feedback controller and the state-feedback gain can be obtained by using the condition. A numerical example is provided to illustrate the main results. Furthermore, an upper bound on the packet loss probability and a lower bound on the SNR guaranteeing the existence of stabilising controller are estimated by exploiting the stabilisation condition in the example.Stabilization problem for networked control systems with random delays using switching and impulsive controllers is investigated. The network-induced delay is modeled as Markov chain and a mode-dependent switching and impulsive controller is introduced for the networked control systems. The necessary and sufficient conditions on the existence of stabilizing controllers are established. An iterative linear matrix inequality approach is employed to calculate the state-feedback gains.Also, this dissertation considers stabilization of wireless networked control systems with packet losses using quantized control and optimal design of quantizer. Random packet losses occur in both sensor-controller link and controller-actuator link. By modeling the packet losses as independent and identically distributed (i.i.d.) Bernoulli processes, the WNCS can be expressed as a Markov jump linear system. Based on the supposed model, we show that the coarsest quantizer that stabilizes the WNCS is logarithmic in the sense of mean square quadratic stability and the stabilization of this system can be transformed into the robust stabilization of an equivalent uncertain system. Moreover, a method of optimal quantizer/controller design in terms of linear matrix inequality is presented.Problems of the quantized stabilization for event-triggered networked systems with packet losses are addressed. To reduce the communication resources in NCSs, event-triggering scheme is adopted and designed.A NCS model is proposed which considers quantization, plant uncertainty, event-triggering scheme and packet losses simultaneously. Sufficient conditions for the stabilization and control design are derived using the Lyapunov functional approach and control synthesis of event-triggered networked control systems are established in terms of linear matrix inequalities (LMIs). Moreover, the maximal allowable number of successive packet losses in NCS is predicted.Finally, a summary for all discussions is given in the dissertation. Future works that related to this work are also presented.