Control Of Complex Dynamical Networks With Random Coupling

Control study of complex dynamic networks is one of the most famous problems in the world.In the real world, because of the differences between the networks topology model and the realstructure, the influence caused by the change of environment temperature and humidity and therandom factors in the impact in network communication, the random factors of complex dynamicnetworks is an objective reality. And the effects of random factors on systems can not be ignored.Therefore, it is necessary to build a stochastic complex dynamic network model which is closely toactual situation as far as possible, and to use different methods of analysis and control strategies tospecific problems. In view of this, we committed to the study of control problems of complexdynamic networks with random coupling, which is of great significance to the understanding andapplication of complex networks. The main research contents in this paper are as follows:First, a model of complex dynamic networks with random time-delays coupling andcommunication noise is designed and presented. The time delays will be described in Markov chain.A novel control strategy is proposed to make complex dynamical networks asymptotically stable,and meet a certain H performance constraint. With using Lyapunov stability and H controlmethod, a controller existing criteria can be derived. The simulation results testify that the controlstrategy is valid.Second, a model of complex dynamic networks with random time-delays coupling andBrownian motion is designed and introduced. These nodes’ information occur delay during theprocess of transmission in complex dynamic networks and the process of delay will be described asa Markov chain. A pinning control strategy is proposed to make complex dynamical networksasymptotically stable. By using Lyapunov stability and It formula, a controller existing criteria canbe derived. The numerical simulation results show that the pinning control method is valid, andexplore the influence of coupling strength to the effect of control.Third, a model of complex dynamic networks with random data-packet dropout is designedand investigated. These nodes’ information which occur delay during the process of transmissionwill be discarded in complex dynamic networks and the process of delay will be described as aMarkov chain. The networks will be asymptotically stable by using pinning control strategy. Withusing Lyapunov stability, a controller existing criteria can be established, and verified by numericalsimulation results, and discussed impact of the probability of data-packet dropout to the effect of control.