中文摘要：

针对混沌系统的控制问题,人们已经提出了很多控制方法。但是,大多数文献在混沌系统控制的设计中,未同时考虑系统参数由于内部噪声等未知扰动的影响而在有界范围内波动的情况,这就导致一些研究结果在实际应用中受到许多限制。因此,研究含参数扰动混沌系统的控制问题是当前混沌控制理论和应用的前沿课题之一。文中以含参数扰动的Liu混沌系统为例进行研究,采用反步设计自适应控制方法对该系统进行控制。首先从系统的反步设计控制理论出发,研究了基于反步设计法、Lyapunov稳定性定理及自适应控制系统控制律,讨论了系统满足设计要求的虚拟控制和控制律的时间响应,确定了同步控制器的结构和控制k的取值范围为47.716 0〈k〈57.222 2时,控制系统渐近稳定;然后根据所设计的含参数扰动Liu混沌系统的反步自适应控制器,得到了含参数扰动的Liu混沌系统在两种不同的情况下的不同控制器,实现了混沌系统在含有未知扰动下的跟踪及镇定控制。该方法在逆推设计过程中结合了反步设计法、Lyapunov稳定性定理及自适应控制律,使系统状态在每一步都能自适应跟踪并渐近趋近虚拟控制,有效地克服因各种未知扰动而产生的参数波动的情况,最后实现整个系统的渐近稳定。理论推导与数值模拟结果验证了控制器的有效性。

英文摘要：

Athough there have been many researches of chaos control,however,few of these researches concern about the control of the parameters perturbation chaotic system in controller design.Therefore,these controllers are not applicable in many actual systems.Therefore,research on the controlling of the parameters perturbation chaotic system is important.The controlling of the parameters perturbation Liu chaotic system was studied in this paper.Firstly,the control theory based on adaptive backstepping technique and Lyapunov stability theorem were described,the time response of virtual control and control law was discussed and the structure of synchronization controller was designed.The system was asymptotically stable when 47.716 0k57.222 2.Secondly,two different controllers were designed in different conditions according to the control theory.The parameters perturbation Liu chaotic system was asymptotically stable under the control of these two controllers.The system＇s state was controlled to follow the virtual control commendably by using the adaptive backstepping technique and Lyapunov stability theorem.Finally,numerical simulations were given to illustrate the effectiveness of the proposed controllers.The result of the paper was proven reasonable by the theory analysis and numerical simulations.