Research On Analysis And Synthesis Of Several Classes Of Stochastic Dynamical Neural Networks With Time Delay

The study of stochastic recurrent neural networks with time delay has been one of hot topics in the nonlinear field. The most applications of neural networks (e.g., optimization, associative memory, image processing and pattern recognition) are related to the dynamic networks behaviors. Compared with delayed neural networks without stochastic disturbance, stochastic delayed neural networks model is more convenient to express practical plant, more complex in the dynamic networks behaviors and more practical in application. Furthermore, in practical industry process, most stochastic disturbance are not satisfied the Gaussian distribution. This motivates the proposition of stochastic distribution control method, which has been received increasing attention. As concerned above, in this dissertation, by employing stochastic delayed differential equation theory, free weight matrix method and linear matrix inequality (LMI) technique, the dynamical analysis of stochastic neural networks with time delay and stochastic distribution control method are investigated, respectively. Some novel methods and ideas in the fields of investigated systems are proposed. The main contents of the dissertation can be briefly described as follows:1. Robust stability problem of a class of stochastic neural networks with interval time-varying delay is studied. Based on stochastic Lyapunov functional theory and free weight matrix method, delay-interval-dependent stability criterion of a class of nominal stochastic delayed neural networks is given. The stability conditions are independent on the delay derivative and applicable to the fast time-varying system or non-differentiable time-varying system. The proposed methods are extended to the stochastic delayed neural networks with either norm-bounded uncertainties or polytopic uncertainties.2. Robust stability problem of a class of Markovian jumping stochastic neu-ral networks with multiplicative noise and time-varying delay is investigated. An extended Ito Isometry Lemma is proposed to deal with the problem of correlation between different noises. A mode-dependent robust stability condition of Markovian jumping stochastic delayed neural networks with multiplicative noise is derived in LMI. 3. The robust stability problem of a class of uncertain stochastic neural net-works with time-varying delay, which satisfies Bernoulli distributed sequence, is concerned. First, a new model of stochastic delayed neural networks is constructed, and the information of delay-probability-distribution is introduced into the param-eter matrix of the new model. Based on probability theory and stochastic analysis method, a delay-probability-distribution-dependent sufficient condition is obtained. Compared with the existing results, the new proposed method eliminates the con-straint on the upper bound of the delay derivative, which can lead to less conservative results.4. The passivity problem of a class of stochastic neural networks with time-varying delay is considered. First, the definition of stochastic passivity is given. Next, based on stochastic Lyapunov functional theory and an improved inequal-ity technique, a delay-dependent passivity criterion with less conservatism is ob-tained. As a special case, passivity condition for the delayed neural networks without stochastic disturbance is given simultaneously.5. The exponential synchronization problem of a class of chaotic stochastic neural networks is investigated. Based on the theory of drive-respond chaos syn-chronization and stochastic analysis method, the condition of the exponential syn-chronization of two identical chaotic stochastic delayed neural networks is obtained, the feedback gain matrix is solved by LMI technique. The proposed method is more precise than other methods in theory, and may be applied to a wider class of applications.6. The probability density function (PDF) tracking control problem of non-Gaussian stochastic distribution systems with input delay is concerned. The B spline neural network expansion and nonlinear weight delay model are prosed to approximate the output PDF, and the problem of PDF tracking control is trans-formed into that of nonlinear weight tracking control. By designing a generalized PI controller, the sufficient condition for stability of closed-loop system is derived to ensure the tracking performance.Finally, concluding remarks are given. Some unsolved problems and devel-opment directions for stochastic neural networks with time delay and stochastic distribution system are illustrated. Further, the prospects of the future study are given.