Wang Shaojie, Yousefpour Amin, Yusuf Abdullahi, Jahanshahi Hadi, Alcaraz Raúl, He Shaobo, Munoz-Pacheco Jesus M
College of Electrical and Information Engineering, Shaoyang University, Shaoyang 422000, China.
School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran 11155-4563, Iran.
Entropy (Basel). 2020 Feb 27;22(3):271. doi: 10.3390/e22030271.
In this paper, dynamical behavior and synchronization of a non-equilibrium four-dimensional chaotic system are studied. The system only includes one constant term and has hidden attractors. Some dynamical features of the governing system, such as invariance and symmetry, the existence of attractors and dissipativity, chaotic flow with a plane of equilibria, and offset boosting of the chaotic attractor, are stated and discussed and a new disturbance-observer-based adaptive terminal sliding mode control (ATSMC) method with input saturation is proposed for the control and synchronization of the chaotic system. To deal with unexpected noises, an extended Kalman filter (EKF) is implemented along with the designed controller. Through the concept of Lyapunov stability, the proposed control technique guarantees the finite time convergence of the uncertain system in the presence of disturbances and control input limits. Furthermore, to decrease the chattering phenomena, a genetic algorithm is used to optimize the controller parameters. Finally, numerical simulations are presented to demonstrate the performance of the designed control scheme in the presence of noise, disturbances, and control input saturation.
本文研究了一个非平衡四维混沌系统的动力学行为和同步性。该系统仅包含一个常数项且具有隐藏吸引子。阐述并讨论了该控制系统的一些动力学特性，如不变性和对称性、吸引子的存在性和耗散性、具有平衡平面的混沌流以及混沌吸引子的偏移增强，并针对该混沌系统的控制和同步提出了一种基于干扰观测器的具有输入饱和的自适应终端滑模控制（ATSMC）方法。为了处理意外噪声，在设计的控制器中加入了扩展卡尔曼滤波器（EKF）。通过李雅普诺夫稳定性概念，所提出的控制技术保证了不确定系统在存在干扰和控制输入限制的情况下的有限时间收敛。此外，为了减少抖振现象，使用遗传算法对控制器参数进行优化。最后，给出了数值模拟，以证明所设计的控制方案在存在噪声、干扰和控制输入饱和情况下的性能。
