The State Estimation Of Complex Dynamical Networks

The rapid development of information technology not only provides the possibility of achievinglarge-scale complex dynamical networks, but also brings great challenges to the existing studies ofcomplex dynamical networks. In the most previous research literatures, all state variables arerequired to construct the controllers for synchronization and topology identification. However, for alarge scale network, measuring all states variables is not easy or even impossible due to complexityof the network, and the limitation of bandwidth, communication mechanism, working environmentand so on. Usually, we can only get parts of the state variables, and the node coupling can only beachieved through the parts of the state variables. In the thesis, in order to get all of the statevariables, and to understand the behavioral characteristics of a complex network better, we studythe state estimation problem of complex dynamical networks, where the controller is designed byusing outputs of networks. The main research contents are as follows:Firstly, under noisy transmission channel, the state estimation of state coupling complexdynamical networks with timev-arying delay coupling is studied in this part. In order to suppressnoise in the channel, the state estimation controllers are designed by using integral control approachwith outputs, a sufficient condition for state estimation is derived by using Lyapunov stabilitytheory andH H control technique. Two simulations are given to verify the effectiveness of theproposed method. under the time-varying coupling and noisy transmission channel, the sateestimation of complex dynamic network coupled with outputs is studied. The sufficient conditionsof state estimation with channel noise and time-varying delay are given in form of linear matrixinequalities (LMIs). Numerical simulation in a scale-free and small world network is given to verifythe effectiveness of the designed scheme.Secondly, due to the complexity of practical networks, the interplay of nodes usually cannot bedescribed accurately by linear functions. The state estimation of nonlinear coupling and nonlineartime delay coupling complex dynamic are studied respectively. A sufficient condition for stateestimation is derived by using Lyapunov stability theory. The criteria are further transformed to theLMIs form. Some numerical simulations are given to verify the effectiveness of the designedcontrollers.Thirdly, on the basis of the third point, considering the influence of noise to the observer, thestate estimation of two models described in third section are studied. By using Lyapunov stability theory andH_H control technique, some sufficient schemes for state estimation are derived in theform of linear matrix inequalities (LMIs), which can make the estimation errors bounded withH performance index. Finally, we take the scale-free network as the network topology and theLorenz chaotic system as the node dynamics, to do some simulations. The simulation results verifythe effectiveness of the proposed method.