The State Estimation Of Complex Dynamical Networks With Time Delays

In the actual complex network, in order to effectively implement system monitor, system adjustment, fault diagnosis and so on, it appears especially important to obtain the network states. However, it is very difficult to measure all the states of the network, and only partial states or outputs can be measured directly. So the state estimation problem of complex networks is that how to determine the other states of the network by using the partial available outputs. The studies of state estimation in the field of complex networks are just starting. This paper focuses on the research of the state estimation of complex networks with time delays. The main research contents are as follows:Firstly, the reduced-order state estimation for state coupling and nonlinear complex dynamical networks with time-varying delays is studied in this part. In practical engineering, partial states of network can be directly obtained through available outputs, which need not to be estimated. The dimensions of the reduced-order state estimator are less than the full-order one, and the structure of it is relatively simple. By employing the Lyapunov-Krasovskii functional, a sufficient condition for reduced-order state estimation is derived that ensure the existence of the desired estimator. Finally, this paper takes BA scale-free network and small-world network respectively as two typical models to demonstrate the feasibility of the proposed method.Secondly, considering the influence of disturbances to the state estimator, the robust state estimation problem for a class of discrete-time networks with multiple time-varying delays and disturbances is studied. And this paper aims to design a robust reduced-order state estimator to estimate the states of the network such that, for time delays and the disturbances, the dynamics of the estimation error is guaranteed to be globally stable and the states of the error system satisfy?H performance. By employing the Lyapunov-Krasovskii functional and?H control approach, a sufficient condition for state estimation is derived that ensure the existence of the desired estimator. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.Thirdly, the problem of guaranteed cost state estimation for output-coupling complex network with time-varying delays is studied. The considered networks are coupled with outputs rather than states due to the fact that only partial states are available. The performance of state estimation is deteriorated by time delays. So this paper aims to design a guaranteed cost state estimator to estimate the network states such that, for time-varying delays, the dynamics of the estimation error is guaranteed to be globally stable and the performance deterioration of state estimation does not exceed a certain upper bound. By employing the Lyapunov-Krasovskii functional, a sufficient condition for state estimation is derived that ensure the existence of the desired estimator. Two numerical example are provided to illustrate the effectiveness of the proposed estimator design scheme.