Cooperativity Analysis And Coordination Control For Complex Networks In Complex Environment

The rapid development of information technology has promoted the vigorous de-velopment of network technology represented by the Internet.These tangible or intan-gible complex systems exist in different forms in the real world and affect all aspects of human life.Theoretically,these complex systems can be abstracted into a group of individuals that interact in complex ways,that is,complex networks.In order to deeply understand the essential characteristics of complex networks and make them more effective for human use,researchers have defined coordination for complex net-works in a given subject environment(mathematics,physics,systems science,computer science,etc.),which means that various components and modules in networks coordi?nate with each other to form a harmonious and orderly combination and complete the task.Further,under the impetus of relevant theoretical perfection and the development of network technology applying to industrial control field,there has been a worldwide upsurge of research interest in complex network dynamics analysis.However,the fractional characteristics,uncertainties,random noise,time delay and external disturbances in complex environments will anffect the cooperativity of complex networks more or less.The main impacts include increasing the difficulty of achieving coordination,disrupting the consistent state and reducing the stability region.In order to analyze the influence mechanism of complex environment on cooperativity of complex network and explore the strategies of dealing with environmental complexity,this paper applies fractional calculus theory and stochastic differential equation theory to establish the criterion on cooperativity of systems and design reasonable control protocols to realize coordination efficiently.The specific work of this paper is as follows:1)Fractional calculus is used to model complex networks in complex environments with fractional properties(including dust storms,polymer fluids,etc.)and to analyses cooperativity of fractional systems.Firstly,the pinning synchronization of fractional complex networks with time delay is studied.The sufficient conditions for the system to achieve pinning synchronization are given.The influence of time delay on the sys-ten is also discussed.Then,for the fractional multi-agent system,by designing a more reasonable and effective adaptive controller,the dependence of the controller parame-ters on the global information of the system is avoided.Based on the fully distributed control protocol,fractional stability theory is applied to establish the consensus criteria.Finally,the numerical simulation is presented to demonstrate the easy realization and universality of the derived criteria.2)For fractional multi-agent systems with external disturbances,from simple to complex,some sufficient conditions are derived based on fractional Lyapunov method to achieve robust consensus in linear systems,nonlinear systems and the systems with or without reference state.Also,the region where the system finally achieves consen-sus is determined,and the influence of external disturbance intensity on the system steady state is discussed.By exploring the influence mechanism of network structure characteristics on network cooperativity,the quantitative relationship between external disturbance intensity and system cooperativity is revealed.The obtained results have certain practical significance.3)Based on the mechanism of sampling control,a reasonable distributed event-triggered control algorithm is designed to achieve consensus of fractional multi-agent systems.Firstly,the specific form of the event-triggered condition is given for the frac-tional multi-agent system.Also,by proving that the time interval between two adjacent trigger events is positive,Zeno behavior can be precluded to ensure the feasibility of the devised event-triggered strategy.Furthermore,in order to avoid keeping track of the measurement errors continuously,a self-triggered strategy is designed,in which the next update time instant of each agent can be computed by using its local history state information.By applying the proposed self-triggered algorithm,the state sampling time is generated and the controller is updated with the sampling state to achieve consensus.Then,the design problem of distributed event-triggered control mechanism for fraction-al systems with control saturation and external disturbances is considered.Based on a low-gain output feedback method,a distributed event-triggered strategy is proposed to utilize in fractional multi-agent systems,under which the network can achieve semi-global consensus.Finally,the effectiveness of the control protocol is demonstrated by numerical simulation,and the applicability of the control protocol in real industrial systems is revealed.4)The influence mechanism of uncertain topology and random noise on the event-triggered coordination of complex network is investigated by using stochastic calcu-lus.For the stochastic discrete complex network and stochastic continuous multi-agent system,respectively,the correctness of the control strategy is proved by designing an effective event-triggered control protocol and applying stochastic differential equation theory.Then,based on the linear matrix inequality,the sufficient conditions for the sys-tem to achieve mean square synchronization under the influence of random noise are given.Furthermore,for the systems with reference signal,the cooperative performance of the system under the corresponding event-triggered control strategy is studied.Fi-nally,the influence of random noise intensity on system coordination is discussed in numerical simulation,and the robustness of the designed control protocol is demon-strated.