Robust Control And State Estimation For Several Classes Of Delayed Neural Networks

In recent years,the theory of neural networks(NNs)have been developed rapidly.The theory has been improved,and the application scope become more and more wide.As is well known,neural networks are required to be stable in application.When implementing a neural network,the occurrence of time delay is unavoidable in the process of storage and transmission.Since the existence of time delay is usually the main sources of instability and oscillations,time delay should be considered in the mathematical model of NNs.Lyapunov stability theory is the basic method to study the stability of NNs.Based on the stability theory,this dissertation studies the problem of robust control and state estimation for delayed NNs.The contents are shown as follows.1.The problem of robust stabilization and H_? control for a class of uncertain neural networks with time-varying delay have been considered.And the design method of robust stabilization controller and H_? controller are obtained.By constructing a novel Lyapunov-Krasovskii functional that contains multiple integral terms,improved delaydependent conditions were established for the robust stabilization problem.Our derivation makes full use of the information of activation function together with the idea of second-order convex combination and the property of quadratic convex function,which reduces the conservatism of the results.We also introduce free-weighting matrix based on the system equation.And we further design a robust H_? controller which guarantees the robust stability of the uncertain neural networks with a given H_? performance level.Finally,numerical examples are given to demonstrate the effectiveness of the design criteria for the robust stabilization controller and the H_? controller.2.The problem of robust stabilization and H_? control for a class of uncertain neural networks with mixed time delays have been solved.And the design method of robust stabilization controller and H_? controller are obtained.By constructing a novel LyapunovKrasovskii functional that contains multiple integral terms,improved delay-dependent conditions were established for the robust stabilization problem.We consider a variety of activation functions,thus the obtained results are more universal.A set of inequalities is obtained under the constraint of activation functions.Our derivation makes full use of the idea of second-order convex combination and the property of quadratic convex function,which reduces the conservatism of the results.Thus,the controller design method can deal with the more large time delay case.Furthermore,our result was extended to the design of a robust H_? controller,which guarantees the closed-loop system robustly asymptotically stable with a prescribed H_? performance level.Numerical examples are given to demonstrate the effectiveness of the design criteria for the robust stabilization controller and the H_? controller.3.The problem of H_? state estimation for a class of delayed static neural networks have been investigated.And the design method of state estimator is obtained.We consider the range of delay varies in an interval for which the lower bound is nonzero,it is more general and more applicable.Some improved delay-dependent conditions are established by introducing delay partitioning method and constructing augmented LyapunovKrasovskii functionals.The state estimator guarantees that the dynamics of the error system is globally exponentially stable and has a prescribed H_? performance.A set of inequalities is obtained under the constraint of activation functions.Our derivation makes full use of the free-weighting matrix approach and reciprocally convex technique,which play an important role in reducing the conservatism of conditions.Numerical examples are provided to illustrate the effectiveness of the proposed method compared with some existing results.4.The problem of H_? state estimation problem for static neural networks with timevarying delay have been investigated.And the further design method of state estimator is obtained.We change the delay partitioning interval and chose novel LyapunovKrasovskii functionals.Some improved delay-dependent conditions are established by using the less conservative integral inequality.A set of inequalities is obtained under the constraint of activation functions.Our derivation also introduce free-weighting matrix based on the system equation,which play an important role in reducing the conservatism of conditions.The gain matrix and the optimal performance index are obtained via solving a convex optimization problem subject to LMIs(linear matrix inequality).The numerical examples show that the proposed method is feasible and superior compared with other literatures.5.The problem of the problem of generalized 2 state estimation for a class of delayed static neural networks have been investigated.And the design method of state estimator is obtained.The state estimator guarantees that the dynamics of the error system is globally exponentially stable and has a prescribed generalized 2 performance.By constructing augmented Lyapunov-Krasovskii functionals,some improved delay-dependent conditions are established by using delay partitioning method and the free-weighting matrix approach.Finally,numerical examples are provided to demonstrate the effectiveness of the results obtained in this dissertation.