Discontinuous Control And Synchronization Of Neural Networks With Time Delays

Discontinuous control of nonlinear systems has been a hot topic in the field of control. Recently, as special class of discontinuous control of nonlinear systems, discontinuous control of neural networks with delayed gets a lot of attention. Discontinuous control of delayed neural networks mainly consists of a variety of right discontinuous systems, such as: neural network systems with delayed under impulsive control, switching neural network systems with delayed, neural network systems via intermittent control hybrid control systems. Recently, delayed neural networks have been applied in many fields, such as image processing, pattern recognition, associative memory, signal processing, optimization, and secure communication. Therefore, the research of discontinuous control of delayed neural networks is a very important topic. Especially, dynamics behavior of delayed neural networks was thorough studied under the hybrid effects of stochastic perturbation, impulsive control, intermittent control, system switching, and obtain some important results.The dissertation focuses on analysing stability and synchronization of neural networks, such as: linear coupling stochastic neural network, nonlinear coupling stochastic neural network, memristor-based neural network, and inertial BAM neural network. The main contributions and originality contained in this dissertation are as follows:â‘  Stability and synchronization of linear coupling neural networks with time-vary delay and stochastic perturbations were presented. It is divided into two parts: 1) we consider coupled switched delay neural network with stochastic perturbation and impulsive effects, got a new impulsive differential equation, and constructed an error systems. Based on the Lyapunov functional method, the comparison principle, and linear matrix inequality technology, we drived some sufficient synchronization conditions of nonlinear system; 2) in the second part, we focusesed on analysis dynamics of the hybrid effects of Markovian switching, stochastic perturbation, impulsive delay on neural networks. First, some novel generic criteria for Markovian switching neural networks with stochastic perturbation and impulsive delay were derived by establishing an extended Halanay differential inequality on impulsive dynamical systems. Second, based on M matrix method, we discussed synchronization of the network, and avoided building an error system. Last, our sufficient conditions ensuring the synchronization are dependent on coupling and impulsive delay and show coupling and impulsive effects on the syn-chronization of neural networks.â‘¡ We investigated another form of discontinuous control: intermittent control. This paper is divided into two parts invistgated intermittent control: the part considers intermittent control is aperiodically, and the other periodically. In chapter 4, we study global exponential stability problem for inertial BAM neural networks with time-varying delay via periodically intermittent control. By utilizing suitable variable substitution, the second-order system can be transformed into first-order differential equations. We can obtain effective condition of exponential stability of nonlinear system by constructing a common Lyapunov functional, and using linear matrix inequality. In the fifth chapter, stability of nonlinear coupled neural networks with time-vary delay and stochastic perturbation is studied. Stability condition of synchronization error system was obtained, ensuring the asymptotic synchronization of nonlinear coupled neural networks with time-vary delay and stochastic perturbation, by designing appropriate aperiodically intermittent controller, and finding a reasonable assumption of nonlinear coupled. In addition, in order to realize synchronization of neural network through adaptive aperiodically intermittent control, we designed reasonable updating laws.â‘¢ Recently, memristor-based neural networks have attracted increasing attention. When memristor realized successfully, it will be a revolution in science and technology. Based on previous research, we constructed complex network model of a linear coupled memristor-based neural recurrent networks with time-vary delay, where stability and synchronization were investigated under discontinuous control of delay impulsive and intermittent. By constructing effective impulsive delay controller, obtained stability condition of synchronization error system. In addition, exponential synchronization of the nonlinear system was invistigated by utilizing M matrix method, and under external and delay impulsive dual control. Meanwhile, we also designed a periodically intermittent controller, and obtained the stability and synchronization efficient condition of coupled memristor-based recurrent neural networks with time-varying. According to the analysis, we have got feasible region of intermittent control parameters, which the designing of the controller provided a better numerical foundation.