Sliding Mode Control For Singular Complex Network Systems

A complex network is defined as a set of nodes interconnected by edges,where each node represents a subunit.Over the past few decades,complex network systems have attracted a great deal of attraction from different fields of scientific research such as the Internet,electricity distribution networks,biological networks and so forth.Meanwhile,in practical situations,complex network systems can model large numbers of systems,thus,the research on complex networks has not only the profound meanings in theory,but also the potential applications in real systems.Descriptor systems contain the normal systems as a special case and can represent a much wider class of systems than the normal systems.Many practical systems can be easily described by the form of descriptor systems.Recently,the theories and practical applications of descriptor systems have attracted much attention of many scholars both in China and abroad,and various results and research methods for state space systems have been perfectly extended to descriptor systems.Due to the distinguishing structural features and special characteristics of descriptor systems,the research for descriptor systems has not only profound meanings in theory,but also wide applications in practice.In this thesis we investigate the sliding mode control for normal nonlinear complex networks and nonlinear singular complex networks respectively.We design a novel nonlinear sliding surface for the nonlinear singular complex network system and derive the sufficient condition to guarantee the stability of the system based on the linear matrix inequality.The main contributions of this thesis are summarized as follows:First,we investigate the sliding mode control for normal nonlinear complex network system.Considering the nonlinear dynamics in the system,we use the method based on the differential mean value theorem to transfer the original nonlinear system into a linear parameter varying system,since the robustness of the sliding mode control to the uncertainties,we design the algebraic sliding surface to the linear parameter varying system and proper sliding mode control in order to make sure the reachability of the sliding surface.Further more,we derive the condition to ensure the stability of the equivalent system.Finally,three examples are shown to illustrate the effectiveness of the proposed method.Then,we investigate the nonlinear singular complex network systems in order to cover a wider scope of the practical systems.We still focus on the sliding mode control problem of these kinds of systems.Still,in the beginning we use the method based on the differential mean value theorem to transfer the nonlinear singular system into a linear singular parameter varying system.Then,we design a novel nonlinear sliding surface for the linear singular system,compared with the sliding surface proposed in the existent results,in this thesis the sliding surface is exponent type rather than the algebraic type or the integral type.We introduce two adjustable parameters into the sliding surface and the linear matrix inequality condition.Because of these two parameters the conservatism of the linear matrix inequality is decreased.Further more,we apply this novel sliding surface to the normal complex network systems,this implies that the novel nonlinear sliding surface can be used in both singular systems and normal systems.Finally,four examples are given to illustrate the effectiveness of the proposed method and compared with the existent results,the method in this thesis is faster and the chattering effect is suppressed well.Finally,the main work of the thesis is summarized,and the potential research topics for further work are pointed out.