不确定分数阶时滞混沌系统自适应神经网络同步控制

针对带有完全未知的非线性不确定项和外界扰动的异结构分数阶时滞混沌系统的同步问题,基于Lyapunov稳定性理论,设计了自适应径向基函数(radial basis function,RBF)神经网络控制器以及整数阶的参数自适应律.该控制器结合了RBF神经网络和自适应控制技术,RBF神经网络用来逼近未知非线性函数,自适应律用于调整控制器中相应的参数.构造平方Lyapunov函数进行稳定性分析,基于Barbalat引理证明了同步误差渐近趋于零.数值仿真结果表明了该控制器的有效性.

Synchronization of uncertain fractional-order chaotic systems with time delay based on adaptive neural network control

Time delay frequently appears in many phenomena of real life and the presence of time delay in a chaotic system leads to its complexity. It is of great practical significance to study the synchronization control of fractional-order chaotic systems with time delay. This is because it is closer to the real life and its dynamical behavior is more complex. However, the chaotic system is usually uncertain or unknown, and may also be affected by external disturbances, which cannot make the ideal model accurately describe the actual system. Moreover, in most of existing researches, they are difficult to realize the synchronization control of fractional-order time delay chaotic systems with unknown terms. In this paper, for the synchronization problems of the different structural fractional-order time delay chaotic systems with completely unknown nonlinear uncertain terms and external disturbances, based on Lyapunov stability theory, an adaptive radial basis function (RBF) neural network controller, which is accompanied by integer-order adaptive laws of parameters, is established. The controller combines RBF neural network and adaptive control technology, the RBF neural network is employed to approximate the unknown nonlinear functions, and the adaptive laws are used to adjust corresponding parameters of the controller. The system stability is analyzed by constructing a quadratic Lyapunov function. This method not only avoids the fractional derivative of the quadratic Lyapunov function, but also ensures that the adaptive laws are integer-order. Based on Barbalat lemma, it is proved that the synchronization error tends to zero asymptotically. In the numerical simulation, the uncertain fractional-order Liu chaotic system with time delay is chosen as the driving system, and the uncertain fractional-order Chen chaotic system with time delay is used as the response system. The simulation results show that the controller can realize the synchronization control of the different structural fractional-order chaotic systems with time delay, and has the advantages of fast response speed, good control effect, and strong anti-interference ability. From the perspective of long-term application, the synchronization of different structures has greater research significance and more development prospect than self synchronization. Therefore, the results of this study have great theoretical significance, and have a great application value in the field of secure communication.