Dynamic Parameters And Network Topological Structure Identification Of Delayed Coupled Networks In Noise Environment

In the natural, social and engineering practice, the dynamical parameters and topological structures of a network are also unknown or uncertain. Therefore, in the research about complex network, it is of theoretical significance and application value to infer its unknown parameters and topological structure. Now, a great deal of progress on research about the dynamical parameters and topology structures identification have been achieved. However, for most of the existing research results, the network models focused on deterministic complex dynamical network situation. In fact, the random noise and time delay are prevalent in complex networks, and for different network model may has different method, so the identification of dynamical parameters and topological structures in delay-coupled networks under circumstance noise is still an urgent issue. Based on the theory and technique of the nonlinear dynamic systems, stochastic differential delay equation and impulsive stochastic differential delay systems, this dissertation further discusses the problem that the identification of dynamical parameters and topological structures in delay-coupled networks under circumstance noise by designing the effectiveness control scheme. The main contents and conclusions are as follows:1、Based on the random generalized projective lag synchronization, we suggest an approach to identify the system parameters and topological structure of delay-coupled complex networks under circumstance noise, by constructing an appropriate controller and adaptive update laws. The accuracy of the method is rigorously proved by the LaSalle-type theorem for stochastic differential delay equations. Finally, an example with networks of chaotic oscillator is provided to illustrate our method. The numerical results indicate that not only the unknown network parameters and topological structure can be accurately identify, but also the proposed method is robust against the time delay, the update gain and the network topology.2、In many practical systems, such as computer networks, automatic control systems and telecommunications, impulsive effects are common phenomena due to instantaneous perturbations at certain moments. In fact, impulsive control is a very typical discontinuous control scheme. Because the pulse control occurs only at certain times, the cost will be greatly reduced. Thus, due to the effective, robust, and low-cost of the impulsive control, this part will employ the techniques of impulsive control and adaptive control to infer dynamical parameters and network topology in two delay-coupled complex networks under circumstance noise. By constructing an appropriate adaptive-impulsive control strategy in the response network, the unknown dynamical parameters and topology structure contained in the drive network are to be accurately identified, moreover, the two networks will achieve global exponential synchronization in mean square. Based on the comparison theorem of impulsive stochastic differential delay equations, the accuracy of the proposed identification strategy is rigorously proved. Finally, an example with networks of chaotic oscillators are provided to illustrate the application of the theoretical results. Meanwhile, numerical results indicate that our proposed scheme is robust against the impulsive gain, the update gain and the network topology.