Finite-time Control Of Networked Switched Linear Systems

Switched systems are widely used in many practices due to its capacity of modeling a kind of multi-modal systems and multi-controller systems, some typical applications including spaceflight, power sources, communication and so on. The related research of switched systems has become an important subject in control area. Switched systems are combined of finite subsystems and a switching signal which can schedule or present the switching between these subsystems. Currently, some investigations on the switching signals and complex dynamic subsystems have been conducted and plenty of results have been reported. However, some potential and challenging problems about switched systems still exist. Moreover, how to combine with the modern transmission media, such as network and the switched systems, to fully explore the advantages of switched systems and networked control systems, are another research frontier, and few results have been reported. On the other hand, most of the studies about switched systems have focused on the Lyapunov asymptotic stability, which is defined over the infinite-time interval.However, some dynamic performance of the systems in the finite-time interval is more important, which leads to the research of finite-time stability. Overall, the finite-time performance analysis and synthesize for the network-based switched control systems will be meaningful.Based on the existing results of continuous-time switched linear systems, in this paper, some developments of the non-networked switched systems will be firstly investigated, upon which the networked switched linear systems will be then addressed in the finite-time interval. An actuator-dependent Lyapunov function construction approach is proposed, which can effectively solve the difficulty of asynchronous switching controller;moreover, this developed technique can also provide a potential approach for the following synthesize of network-based switched linear systems. In addition, from the point of reducing the network sources, an event-driven communication approach is also introduced. The aforementioned techniques can provide some feasible scheme for the studies of networked switched systems with complex dynamic subsystems(such as uncontrollable subsystems) and the constricted networks. Some developed theoretical results are also testified by practical applications, such as multi-switching position servo system for the obtained technique of asynchronously switched mode-dependent controller design and the satellite output tracking control system for networked mode-dependent tracking controller design technique. These developments can contribute to the related research of networked switched systems for practical applications. Main results and contributions are as follows.Firstly, the research developments of switched systems in non-networked environment are discussed and some developed techniques are originally presented. For the research of switching signals, four main switching approaches, including random switching,dwell-time, average dwell time and mode-dependent average dwell time are investigated.Moreover, a new persistent-dwell time switching approach is also studied for switched linear systems. For the research of switched systems with complex dynamic subsystems, the uncertain switched systems with polytopic uncertainty and unstable subsystems are addressed and the corresponding finite-time controller are designed. The developed method in this section can be used to solve the controller design problems of switched systems with uncontrollable subsystems. For the synthesize research of switched systems, a novel controller-dependent Lyapunov function construction approach is proposed, which can effectively reduce the difficulties of solving the linear matrices inequality(LMI)-based criteria, it can also provide potential approach for the controller design of the networkbased switched systems. Most of the mentioned developments above can both enrich the current technique framework of switched systems and improve the following research.Then, the network-based finite-time controller design problems for switched linear systems with constricted communication networks are investigated, including statefeedback control, observed-based state-feedback control and output tracking control. By employing the input-delay technique, the constricted communications are firstly reformulated into the time-varying delays of the switched systems. Moreover, the mode-detection and communication delays are also taken into account, which actually leads to the asynchronous switching of the switched time-delay systems. Based on the improved techniques of controller design for asynchronous switching, the admissible switching signals with average dwell time approach and the sufficient conditions are obtained. The considered three control schemes cover the main control approaches in the existing results, the individual and coupled problems for switched systems and networked control systems are both solved, which also provides the potential approaches for the networked filtering and stat estimation problems of switched systems.Moreover, a novel event-driven communication approach is introduced, which contains state-dependent event-driven scheme and hybrid event-driven scheme. The proposed event-driven communication approach can effectively reduce the transmission data. General scheme for networked control systems is transmitting all the sampling data; however,the developed event-driven scheme only transmit the sampling data which satisfy the prescribed event-driven scheme. When the switching signals are known a priorior can be detected and transmitted instantly, the state-dependent event-driven scheme is firstly discussed, i.e., all the sampling state values will be analyzed, only the sampling data satisfy the event-driven scheme, the communication event will be triggered. When the switching signals are unknown or can be detected by sampling, the hybrid event-driven scheme is invoked. This scheme means that, either the state-dependent event is satisfied or the switching occurs and be detected, the data with state/mode information will be transmitted. The state-dependent event-driven scheme and hybrid event-driven scheme are actually for the synchronous and asynchronous switching control problems of networked switched systems. The developed techniques in this chapter can fully explore the state and state variation information to reduce the networked data transmission and optimize the network communication environment.The finite-time controller design problems for the networked switched systems with uncontrollable subsystems is also studied. The nonuniform sampling and hybrid eventdriven communication scheme are both taken into account. A new switching law which has the maximum ratio of the activation intervals of uncontrollable and controllable subsystems is proposed. Combined with the average dwell time approach, the finite-time performance for the switched systems with complex dynamic subsystems and complicated sampling and transmission can be derived. The developed results in this chapter are the combination of the finite-time controller design of switched systems with unstable subsystems, the developed asynchronous switching controller design, and the hybrid eventdriven communication. The results can provide a kind of potential approaches for the studies of the networked switched systems with stochastic sampling and/or constricted communication networks.