Research On Complex Network Synchronization Via Distributed Pinning Impulsive Control

Complex network has the typical interdisciplinary characteristics.Due to the dynamic characteristics of its nodes and the mutual influence transmitted by couplings,it is widely used in the modeling of biology,sociology,computer science and other disciplines.Synchronization,as an important swarm behavior in complex networks,has received extensive attention from scholars.For the network models that cannot realize convergent behavior through couplings,control inputs are used to help to achieve synchronization,among which,impulsive control method has received widespread attention for its high efficiency.On this basis,the pinning impulsive strategy and distributed strategy are applied to save control costs by reducing the number of controlled nodes and the required state information,respectively.With regard to the research on complex network synchronization,the performance of hybrid impulse sequences in synchronization problems,the influence of the quantization relationships between time delay scales and impulsive intervals on synchronization,the function of pinning impulsive strategy in the secure synchronization issues,and other unanswered questions,all inspire us to carry out related research.The main contributions are summarized as follows:(1)For a class of nonlinearly coupled complex networks with time-varying delays and stochastic disturbances,considering that networks would subject to certain impulse disturbances,a kind of distributed control schemes combined pinning control and impulsive inputs is discussed to realize exponential synchronization.Based on the concept of average impulsive interval,sufficient conditions for achieving the exponential synchronization are derived.In addition,the exponential convergence velocities are obtained,respectively,regarding to different functions of the impulsive inputs.(2)For a class of nonlinearly coupled complex networks with multiple time-varying delays,a distributed controller is introduced for realizing the exponential synchronization of the complex network with different delay scales that are known in advance.Lyapunov stability theorem and mathematical induction method are used to obtain delay-dependent criteria for global impulsive synchronization.Additionally,an adaptive strategy is adopted to establish appropriate impulsive intervals suitable for the complex networks with prior unknowable delays.The fact that the proposed adaptive scheme is more general and less conservative enables the effective release of the constriction caused by unknown delay scales.(3)For a class of cyber-physical complex networks with deception attacks,the false data caused by which is assumed to be injected into both the sensor-to-controller channels and the controller-to-actuator channels,which is modelled by Bernoulli stochastic variables.A distributed controller combined with impulsive protocol is applied for realizing the secure synchronization.By jointly applying the definition of average impulsive gain,the definition of average impulsive interval and Lyapunov stability theorem,sufficient criteria are obtained to ensure the secure synchronization within the given error bounds.In addition,pinning impulsive method is proposed to describe the attacks on vulnerable systems in complex networks,therefore,the theorem is extended to a less conservative situation.(4)For a class of cyber-physical complex networks suffering from deception attacks,the false data generated by attacks in both sensor-to-controller channels and controllerto-actuator channels is assumed to obey the Bernoulli distribution.By jointly combining distributed impulsive control scheme,time-varying impulsive effects and the self-triggered mechanism,a kind of distributed self-triggered impulsive controllers is elaborately designed.By integrating the definition of average impulsive gain,the contradiction analysis method and Lyapunov stability theorem,sufficient conditions are derived for ensuring the secure synchronization within the upper bound of errors.In addition,for further decreasing the triggering frequency and energy consumption,the novel dynamic self-triggered mechanism is designed.It is worth mentioning that the self-triggered mechanism can be regarded as the special pinning impulsive strategy.Additionally,the updating laws adopted for dynamic self-triggered protocol is non-monotonic,which benefits to deal with the bounded synchronization.(5)For a class of complex networks with nonlinear couplings,distributed time-varying delays and mismatched parameters of individual systems,a kind of leader-following quasi-synchronization issues is analyzed via impulsive control.To acquire appropriate impulsive intervals,the dynamic self-triggered mechanism is devoted to predicting the available instants of impulsive inputs.With the utilization of Lyapunov stability theorem,comparison lemma and the parameter variation method,sufficient conditions for realizing the quasi-synchronization within a specific bound are derived.In addition,with the definition of average impulsive gain,the parameter variation scheme is extended and adopted to the time-varying impulsive effect case.In addition,numerical simulations are given regarding to the theorems proposed in this thesis to verify the feasibility.Several node selection strategies are compared,and the corresponding analyses are carried out.