【作者】 李明；

【导师】 郑永爱；

【作者基本信息】 扬州大学 ， 控制理论与控制工程， 2017， 硕士

【摘要】 混沌理论是非线性科学中重要的研究课题,主要对混沌动力学行为进行深入探索,强有力地解释了自然界和人类社会中的诸多现象。随着分数阶微积分理论的深入研究,混沌系统的研究也推广至分数阶次。分数阶微分方程使得物理模型得到了简化,提升了动力学系统的构造和控制能力。另一方面,由于分数阶混沌系统具有整数阶混沌系统的全部动力学特征,更能直观地表现出问题的实质,在保密通信和控制工程等领域有着巨大的应用前景,因此分数阶混沌系统的同步控制近年来已成为非线性科学领域的研究热点。在本文中,我们对不确定分数阶混沌系统的同步控制问题进行深入理论分析和探讨,将理论分析和数值仿真相结合,证明了所提分数阶混沌系统同步控制新方法是可行的。本文主要取得了如下成果:1.实现了分数阶混沌系统的延迟双同步。基于分数阶Lyapunov稳定性理论,提出一个实现分数阶混沌系统延迟双同步的方法,得到实现分数阶混沌系统延迟双同步的一个充分条件。通过数值模拟仿真,验证了分数阶混沌系统延迟双同步的充分条件是可行的。2.研究了分数阶混沌系统的自适应滑模同步问题。首先构建了具有强鲁棒性的分数阶积分滑模面,然后以此为基础构造了合适的控制器。利用分数阶Lyapunov稳定性理论对所提控制策略的正确性进行分析。数值仿真结果表明了该控制方法可以使分数阶混沌系统实现渐近同步。3.研究了分数阶混沌系统的混合投影同步问题。采用自适应滑模控制方法,明确提出了一种新的同步控制方案,从而使得不确定分数阶混沌系统实现了混合投影同步。通过对分数阶混沌系统进行同步仿真,数值仿真结果证明了该同步控制方案是有效的。更多还原

【Abstract】 Chaos theory is the most important research topics in nonlinear science,it mainly explores the chaotic dynamical behavior,and it explains many phenomena in nature and human society.With the development of research on fractional order calculus theory,the research of chaotic systems also extends to fractional order.The fractional differential equation simplifies the physical model,it improves the construct and control ability of the dynamic system.On the other hand,owing to the fractional order chaotic systems have all dynamic characteristics of the integer order chaotic systems and could show the essence of the real problem intuitively,and it has great application prospect in the field of secure communication and control engineering,so the synchronization control of fractional order chaotic systems has become a hot topic in the field of nonlinear science recently.In this paper,we do some profound theoretical analysis and exploration on the synchronization control problem of uncertain fractional order chaotic systems.Combining theoretical analysis and numerical simulation,we verify the feasibility of the proposed new synchronization control methods for fractional order chaotic systems.The main work of this paper are as follows:1.The lag dual synchronization of fractional order chaotic systems is realized.Based on the fractional Lyapunov stability theory,a lag dual synchronization control method of fractional order chaotic systems is proposed and an sufficient condiction is derived to realize the lag dual synchronization of fractional order chaotic system.By numerical simulation,we verify the sufficient condiction of the lag dual synchronization of fractional order chaotic systems is feasible.2.The adaptive sliding mode synchronization problem of fractional order chaotic systems is studied.Firstly,the fractional integral sliding mode surface with strong robustness is introduced,and then an appropriate controller is designed.The correctness of the proposed control strategy is analyzed based on fractional Lyapunov stability theory.The numerical simulation results show that the asymptotic synchronization can be realized between two fractional order chaotic systems with the proposed control method.3.The hybrid projective synchronization problem of fractional order chaotic systems is studied.A new synchronization control strategy is introduced to realize the hybrid projective synchronization for uncertain fractional order chaotic systems by using the adaptive sliding mode control method.The simulation results of fractional order chaotic systems show the effectiveness of the proposed method.更多还原