Jahanshahi Hadi, Shahriari-Kahkeshi Maryam, Alcaraz Raúl, Wang Xiong, Singh Vijay P, Pham Viet-Thanh
Department of Aerospace Engineering, Faculty of New Sciences and Technologies, University of Tehran, Tehran 14395-1561, Iran.
Faculty of Engineering, Shahrekord University, Shahrekord 64165478, Iran.
Entropy (Basel). 2019 Feb 7;21(2):156. doi: 10.3390/e21020156.
Today, four-dimensional chaotic systems are attracting considerable attention because of their special characteristics. This paper presents a non-equilibrium four-dimensional chaotic system with hidden attractors and investigates its dynamical behavior using a bifurcation diagram, as well as three well-known entropy measures, such as approximate entropy, sample entropy, and Fuzzy entropy. In order to stabilize the proposed chaotic system, an adaptive radial-basis function neural network (RBF-NN)-based control method is proposed to represent the model of the uncertain nonlinear dynamics of the system. The Lyapunov direct method-based stability analysis of the proposed approach guarantees that all of the closed-loop signals are semi-globally uniformly ultimately bounded. Also, adaptive learning laws are proposed to tune the weight coefficients of the RBF-NN. The proposed adaptive control approach requires neither the prior information about the uncertain dynamics nor the parameters value of the considered system. Results of simulation validate the performance of the proposed control method.
如今，四维混沌系统因其特殊特性而备受关注。本文提出了一个具有隐藏吸引子的非平衡四维混沌系统，并使用分岔图以及三种著名的熵度量（如近似熵、样本熵和模糊熵）来研究其动力学行为。为了使所提出的混沌系统稳定，提出了一种基于自适应径向基函数神经网络（RBF-NN）的控制方法来表示系统不确定非线性动力学的模型。基于李雅普诺夫直接法对所提方法进行稳定性分析保证了所有闭环信号是半全局一致最终有界的。此外，还提出了自适应学习律来调整RBF-NN的权重系数。所提出的自适应控制方法既不需要关于不确定动力学的先验信息，也不需要所考虑系统的参数值。仿真结果验证了所提控制方法的性能。
