Synchronization Of Complex Dynamical Networks With Time Delays And Randomly Occurring Phenomena

In recent years, complex dynamical networks have been an active research area due to their theoretical importance and broad applications in the real world. Generally speaking, complex dynamical networks are consisted of numbers of dynamical nodes, which change information according to certain topologies and exhibit collective behaviors. Several typical examples of dynamical networks can be found in the real world, such as the Internet, biological neural networks, electric power networks, social networks and so on.As one of the fundamental issues, the synchronization problem has attracted rapidly increasing attention.It should be pointed out that time delays exist ubiquitously in complex dynamical networks, which include the time delay in the independent node and the time delays of the information exchanges among the interconnected nodes. As is well known, time delays may degrade the synchronization performance of the complex dynamical networks or even destroy the synchronization. Therefore, time delays should be taken into account in the synchronization problem. Moreover, complex dynamical networks often exhibit certain randomly occurring phenomena, such as randomly occurring nonlinearities, randomly occurring time delays, randomly occurring parameter uncertainties and so on. By introducing these phenomena, the model of complex dynamical networks can be better described. Considering the above issues, the main researches of this dissertation deal with the synchronization problem of complex dynamical networks with time delays and randomly occurring phenomena, which can be summarized as follows:For the complex dynamical networks with external disturbances and time-varying delays, the mixed H_∞ and passive synchronization problem is investigated in the driveresponse framework. Based on the mixed H_∞ and passive performance index and by constructing the Lyapunov-Krasovskii function, delay-dependent sufficient conditions are established to ensure that the drive networks can synchronize with the response networks.The simulation results are provided to show the effectiveness and applicability of the designed control method.In the drive-response framework, since it is always very difficult to implement the synchronization controllers by the designed parameters exactly, the synchronization problem of complex dynamical networks with randomly occurring nonlinearities and controller gain fluctuations is concerned. In addition, the time delays in the nodes are considered in the model. By introducing the stochastic variables, the non-fragile controllers are designed to solve the synchronization problem. By utilizing the stochastic analysis,delay-dependent sufficient synchronization criteria are established. The correctness of the obtained theoretical results are demonstrated by a numerical example.The non-fragile H_∞ drive-response synchronization problem of complex dynamical networks with external disturbances is further studied. In particular, the influences of randomly occurring parameter uncertainties and randomly occurring controller gain fluctuations are taken into account to model more realistic dynamical behaviors of the complex dynamical networks. Sufficient synchronization criteria are developed to achieve the prescribed H_∞ performance. Based on the obtained results, a set of synchronization controllers are designed to ensure the synchronization with disturbances. An illustrative example is provided and simulation results show that the developed controllers can achieve the H_∞ synchronization.In addition, the non-fragile controlled synchronization problem for complex dynamical networks is investigated with randomly occurring delayed information exchanges among the interconnected nodes. More precisely, the nonlinear model of the single node is adopted to better describe the dynamical properties of the complex dynamical networks.By applying the Lyapunov-Krasovskii functional method, delay-dependent synchronization conditions are provided. Furthermore, a set of controllers are developed based on the established criteria to guarantee the synchronization. The effectiveness and feasibility of the designed control scheme are verified by the given numerical example.Finally, the non-fragile controlled dissipative synchronization problem for complex dynamical networks with randomly missing data and external disturbances is further concerned. It is worth mentioning that since the phenomenon of missing data always randomly happens in the applications, the stochastic model is adopted to describe this randomly occurring phenomenon. Moreover, the effects of the randomly occurring coupling delays are also considered. By introducing the dissipative performance, the delay-dependent sufficient conditions are established. Based on the conditions, a set of controllers are designed to ensure that the synchronization can be achieved. An illustrative example is given and simulation results show the correctness and effectiveness of the obtained theoretical results.