Abstract
The synchronization of complex networks is one of the key points to study the dynamic law of network. Due to the influence of external environment or physical conditions, nonlinear interference is inevitable. As a result, system parameters will not be obtained completely, which is not conducive to realize synchronization of network. In order to get system state variables and realize synchronization of complex networks with external interference. A synchronization control method is proposed based on the extended observer theory and sliding mode control theory in this paper. Firstly, aiming at the problem that the system state variables can’t be obtained accurately. A method of designing extended observer is proposed to observe the unknown state variables of system. Secondly, on the basis of getting the system state variables, in order to realize system synchronization control, the synchronization controller is designed based on the sliding mode control theory. And the correctness of this method is proved by Lyapunov stability theory. Finally, the validity of the proposed method is verified by simulation of Lorenz chaotic system of random 30-node and IEEE39-bus system.
Highlights
As a basic tool to understand real dynamic behavior systems, complex networks have attracted wide attention in many aspects
In order to realize the synchronization of complex networks with unknown interference and be not restricted to the application condition, a synchronous control method is proposed in this paper
(ii) When the external interference is wi1(t) = wi2(t) = wi3(t) = 10 cos(2t) and the synchronization states are yi1 = 4 cos(4t), yi2 = −6 sin(6t) and yi3 = −5 sin(5t), the simulation results of the synchronous state curves, observation curves, observation error curves and synchronous error curves are as shown in FIGURE 8, FIGURE 9, FIGURE and FIGURE
Summary
As a basic tool to understand real dynamic behavior systems, complex networks have attracted wide attention in many aspects. Even if there are synchronization methods of complex network with external interference, they has some limitations apply. Such as reference [18], the H∞ synchronization control of. In an actual network, there are various interference factors such as random forces in the physical system or noise generated by uncertain factors in the experimental environment [19], their boundaries are usually unknown In order to realize the synchronization of complex networks with unknown interference and be not restricted to the application condition, a synchronous control method is proposed in this paper. The feasibility of this paper method is verified by simulation
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