Research On Several Kinds Of Complex Networks Synchronization Control Problems And Application

Complex networks exist in the colorful world, many complex systems can be described by complex networks, the relationship among the individual of complex systems correspond to the edges properties among nodes of complex network. Usually, two nodes can be connected by an edge if there is a certain relationship between these two nodes and multi-link correspond to multiple relationships between these two nodes.There are many kinds of complex networks in real life, such as transportation network, information network, social network and biological network et al. The research of biological neural network as a special case of complex networks has gradually formed a complete theoretical system, especially in the aspect of artificial neural network to simulate the corresponding working mechanism of biological neural network. In order to more effectively simulate the learning and memory function of biological neural network, the memristor as an equivalent electronic device of nerve synapse is introduced to explore the dynamic behavior of the memristive neural network. Synchronization behavior as a kind of dynamic behavior of cluster is a nonlinear phenomenon of nature.Synchronization behavior is good or bad, the study of synchronization behavior can also avoid the occurrence of harmful synchronization behavior, promote the generation of beneficial synchronization behavior,so as to achieve a multiplier effect in real work. The known or uncertain complex networks as carrier of real life show the colorful synchronization behavior.Due to various of structure and complex dynamical behaviors(bifurcation or chaos behavior) of nodes in complex networks, it is of great practical significance to study the control and synchronization of complex network systems.There have two kinds of control methods in studying on the process of synchronization in complex networks: one is to achieve synchronousation of complex networks by changing some of the properties of complex networks (the network topology and the coupling strength etc.); another is to obtain the desired synchronization of complex networks by using control input and the corresponding control method include strict feedback control, adaptive control, impulse control and intermittent control etc.. Because of the existence of some uncertain factors in information transmission, the delay phenomenon and the influence of stochastic noise which are considered can be well explained the real dynamic phenomena of complex network in the real world, which can solve real specific problems by the corresponding theoretical research results. Considering the problems above, we give the detail definition of synchronization?controller design method and the sufficient conditions of synchronization in different forms of complex networks. Numerical simulations are given to verify the feasibility and effectiveness of the proposed method. First, asymptotic synchronization and finite-time synchronization problem of multi-link complex networks are studied?Then, the parameters identification of uncertain multi-link complex networks are also investigated based on different synchronous control.Finally, we give the corresponding research in the stability and synchronization and anti-synchronization control problem of memristive neural network. The main contents of this paper are as follows:(1) For some multi-link complex networks, we consider asymptotic synchronization and finite-time synchronization problem of multi-link complex networks. Firstly, the modified function projective synchronization of multi-link complex networks is studied. The function matrix as an unpredictability scaling function are definited to enhance security of communication between complex networks. Meanwhile, we consider the uncertain multi-link complex network with stochastic noise and overcome theses difficulties of stochastic influence and uncertain factors to achieve the modified function projective synchronization in the mean square sense, several synchronization criteria are obtained by designing a proper feedback controller and novel adaptive control law. In theory, it shows that this new adaptive feedback controller can guarantee the realization of the stochastic synchronization of complex networks with stochastic noise based on the Lyapunov stability theory and stochastic differential theory. The theoretical analysis is verified by simulation experiments and the adaptive nonlinear feedback controller is proved to be robust. Secondly, achieving synchronization state of complex network as soon as possible can ensure the safety of the data transmission and communication. Therefore, finite-time stability theory is introduced to achieve finite-time synchronization of multi-link complex networks in this paper. Multi-link complex network is divided into many different sub-networks show some interesting dynamic phenomena.We consider two kinds of discontinuous control methods, including intermittent control and impulseive control, to obtain several finite-time synchronization criteria, which not only achieve to synchronization goal,but also reduce the corresponding control cost. Finally, numerical simulations verify the effectiveness of our proposed theoretical analysis;(2) For multi-link complex networks with some unknown information, we consider the issues of the unknown parameters and unknown topology connection respectively. Firstly, the impulsive control method is used to study finite-time synchronization and parameter identification of uncertain multi-link complex networks in this paper.Impulsive control as a kind of effective and ideal control technology can not only realize the synchronization target but also reduce the control cost.This paper presents an impulsive complex network model with uncertain parameters and design two different adaptive feedback controllers to realize exponential synchronization?finite-time synchronization and parameters identification based on impulsive delay differential inequalities controller design. Secondly, we consider the stochastic noise to give two different methods to identify the topological connections and guarantee finite-time synchronization of multi-link complex networks in this paper. Two adaptive feedback controllers are respectively designed to realize the topology identification and finite-time synchronization between the same and different topologies based on the finite-time stability theory and drive-response concept. Finally, numerical simulations verify the effectiveness of theoretical analysis;(3) For memri stive nueral networks, we congsider the anti-synchronization control?finite-time boundedness and finite-time synchronization control problem of memristive neural network. Firstly,since some random factors (internal interference and stochastic noise of external environment) in neural network; since the anti-synchronization phenomenon is ubiquitous in the neural network and has important application; since the parameters of memristive neural network are state dependent, the system stability or synchronization of memristive neural network via the classical analytical techniques are not realized directly. It is of practical significance to study the stochastic anti-synchronization of memristive neural network with the non-modeled dynamics and stochastic noise by establishing a less conservative memristive neural network model and designing the adaptive controller and the corresponding control law based on differential inclusions theory?linear matrix inequality, Gronwall inequality and adaptive control technique to realize the exponential anti-synchronization of memristive neural network in mean square sense. According to the changing environment or the changed environment, the adaptive controller is able to adjust its behavior to obtain better performance, that is, it has a good ability to adapt with the changing environment. Furthermore, a numerical simulation is given to verify the effectiveness of the proposed control method. Secondly,according to the different requirements of network states, the finite-time stability theory is introduced to study the boundedness and synchronization of the memristive neural network. When network states do not need to be strictly stable to the equilibrium point in a finite time,but only remain a bounded interval, a novel technique is first developed to transform the memristive neural network into the form of neural network with interval parameters in the paper. Further by introducing the appropriate Lyapunov function and the concept of finite-time boundedness, a new method is proposed to guarantee that the state trajectory remains in a bounded region of the state space over a given finite-time interval. When network states require strict stability to the equilibrium point in a finite time, we study finite-time synchronization of memristive neural network with impulsive effect and stochastic perturbation based on the above novel conversion technology. The finite-time synchronization is obtained by disposing of parameter mismatch, impulsive effect or stochastic perturbation for the memristive neural network. Several useful criteria of synchronization are obtained based on Lyapunov function, linear matrix inequality (LMI) and finite-time stability theory. Finally, some numerical examples are given to demonstrate the effectiveness of our proposed method.