受扰航天器姿态动力学中参数未知的混沌运动控制

研究了扰动力矩作用下航天器姿态运动的欧拉动力学方程. 讨论了当选取扰动力矩中不同的参数矩阵, 欧拉方程可产生一大类混沌系统. 设计了基于Lyapunov方法的自适应控制律, 完成了该类系统中参数未知的混沌运动的控制, 并且能够将系统状态变量稳定于指定平衡点, 同时实现了对未知参数的实时辨识. 以Newton-Leipnik系统为例, 进行了数值仿真, 仿真结果表明了该方法的有效性. 关键词： 姿态运动 混沌控制 参数未知 Newton-Leipnik 系统     

分数阶Newton-Leipnik系统的动力学分析

依据分数阶线性系统的稳定性理论,研究了具有双重混沌吸引子的Newton-Leipnik系统取不同分数阶时的动力学行为.研究表明该系统具有逆向Hopf分岔过程,即随着阶数的下降,分数阶Newton-Leipnik系统由双重混沌吸引子突变为单吸引子,其动力学行为将由混沌态历经短暂的周期态后收敛于稳定的平衡点.     

一种新的分数阶系统稳定理论及在back-stepping方法同步分数阶混沌系统中的应用

对阶次小于1的分数阶系统的稳定问题,提出了一种新的判据.基于该理论,将back-stepping方法拓展到分数阶系统中并设计控制器实现了分数阶Newton-Leipnik混沌系统的同步.数值仿真验证了稳定性理论的准确性及控制器设计方法的有效性. 关键词： 分数阶 同步 back-stepping方法 Newton-Leipnik     

Feedback control and hybrid projective synchronization of a fractional-order Newton-Leipnik system

In this work, stability analysis of the fractional-order Newton-Leipnik system is studied by using the fractional Routh-Hurwitz criteria. The fractional Routh-Hurwitz conditions are used to control chaos in the proposed fractional-order system to its equilibria. Based on the fractional Routh-Hurwitz conditions and using specific choice of linear feedback controllers, it is shown that the Newton-Leipnik system is controlled to its equilibrium points. Moreover, the theoretical basis of hybird projective synchronization of commensurate and incommensurate fractional-order Newton-Leipnik systems is investigated. Based on the stability theorems of fractional-order systems, the controllers for hybrid projective synchroniztion are derived. Numerical results show the effectiveness of the theoretical analysis.