State Estimation And Filtering Of Delayed Neural Networks

Over the past30years, neural networks have gained many important research results in both the field of theory, such as the stability, periodic solution, fault tolerance, robust-ness of the neural networks, and the field of application, involving in pattern recognition, machine learning theory, optimization problems, signal processing and so on. However, in actual systems, under the limits of transmission rate of transmission medium and response speed of machinery and devices, time-delay occurs in the process of information transmit through neural network. All in all, time-delay is one of the main reasons which usually degrade the system performance and even make the system unstable. So the studies of the stability, state estimation and filtering of delayed neural networks have significant theoretic meaning and application value.As the basic problem in the area of control, state estimation has received research attentions for a long time. But the study on state estimation of neural network only has a short history and many problems and results should be studied widely and deeply. In this paper, we consider the state estimation and filtering problems of three kinds of neural networks, the main results are as follows:(1) The problem of exponential state estimation of discrete-time neural networks with mixed delays, including discrete delay and distributed delay, is considered. The Lyapunov-Krasovskii stability theorem and free weight matrix technique are applied and a sufficient condition is established to ensure the asymptotical stability of the error system. Then by the method of norm analysis, counteracting and exchanging of sum order, the exponential performance of the designed estimation is proved.(2) For a class of static neural networks, a H∞filtering for such delayed neural net-works is considered. Based on the lower bounds theorem, we introduce a new inequality to deal with the time-delays, then the sufficient delay-dependent and delay independent con-ditions are established respectively to ensure the guaranteed H∞performance filtering for the delayed neural networks. In contrast to the previous results concerning this problem, our results are less conservative. Numerical examples are presented to show the effective-ness of the proposed design methods.(3) The problem of L2-L∞filtering for discrete-time Markovian jumping neural networks with missing measurements is considered. Based on the appropriate Lyapunov—Krasovskii functional and some linear matrix inequality techniques, a sufficient condition is established to ensure the guaranteed L2-L∞performance filtering of the Markovian jumping neural networks with missing measurements. In addition, we also provide the sufficient condition for the problem when the measurements of neural network can be fully obtained and delayed states are involved in the missing measurements. What’s more, the problem of measurements transmitted through different channels is studied and a sufficient condition is presented.