Pinning Synchronization Control And Sliding Mode Control For Networked Systems

With the rapid development of network sciences and advanced control technologies,control science,especially those interdisciplines between control science and the related subjects such as electric automation,computer networks,electronic information and so on,have been increasingly paid close attention to by the researchers.As one of the most important applications in network sciences,control theories are always resorted to when dealing with the synchronization problem for complex networks and addressing the stability/convergence problem for dynamical systems.The commonly used control methods include pinning control,sliding mode control and so on.In the study of synchronization of complex networks,through the method of pinning control,synchronization can be realized if only part of the network nodes are selected/controlled reasonably,so as to release the restrictions on the communication topology of the network.Control theories also play an important role when solving the engineering problems.In fact,many problems involved in engineering can be described mathematically by differential systems,which in practice,are inevitably influenced by a great deal of uncertainties such as nonlinear external interferences,measurement errors and so on.As one of the most important control methods,sliding mode variable structure control has many excellent properties,such as its insensitivity to parameter variations,the effective resistance to external disturbance,easy manipulation and so on.Hence,the sliding mode control strategy is always resorted to when solving the control problems.Stability is one of the most basic problems in control theory,and the research on synchronization problem between the network nodes and the target one can be eventually converted into the stability investigation for the error dynamical systems.Therefore,this paper mainly focuses on the research of pinning synchronization for complex networks,and then by the sliding mode variable structure control strategy,the system under study is to admit the property of strong robustness.Based on these discussions,the main work of this paper is summarized as follows:Firstly,the problem of pinning synchronization is investigated in this paper for a class of directed complex networks with Lorenz-type nodes and periodic intermittent communication.By utilizing the Lyapunov stability theory and the theories on M-matrix,some interesting criteria are obtained which clearly address what kinds of nodes and at least how many nodes should be chosen and pinned for synchronizing the whole network.It is theoretically shown that the global pinning synchronization of the considered network with intermittent interactions can be realized if the augmented network topology contains a directed spanning tree,the communication rate is larger than a threshold value and the coupling strength among neighboring nodes is suitably selected.A numerically example is finally given to verify the effectiveness of the theoretical results obtained.Secondly,in the light of the finite time sliding mode control schemes and the fixed-time sliding mode control method for second order systems,this paper is devoted to investigate the fixed-time sliding mode control problem for high order linear perturbed systems.A series of fixed-time sliding surfaces and the sliding mode control law are designed to make the high order system under study achieve the fixed-time stability.When designing the high order fixed-time control law,in order to avoid the phenomenon of singularity,initial condition of the system is confined in this paper to guar-antee the boundedness of the control law.