一类脉冲动力系统的状态反馈控制  

STATE FEEDBACK CONTROL OF A CLASS OF IMPULSIVE DYNAMIC SYSTEMS

作　　者：蒋贵荣[1] 陆启韶[1] 钱临宁[1] 

机构地区：[1]北京航空航天大学理学院

出　　处：《动力学与控制学报》2005年第4期17-23,共7页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(10432010;10172011)~~

摘　　要：对一类具有状态反馈控制的脉冲动力系统的动力学性质进行了研究.由周期解的扰动解得到了一个Poincare映射,利用Poincare映射讨论了系统周期解的分岔,并得到了半平凡周期解和正周期1解存在和稳定的充分条件.定性分析和数学模拟表明,半平凡周期解通过fold分岔分岔出正周期1解,正周期1解通过flip分岔分岔出正周期2解,再通过一系列flip分岔通向混沌.此外,讨论了脉冲状态反馈控制的效果.The dynamics of a class of impulsive dynamic systems with impulsive state feedback control was studied. A Poincare map was constructed to discuss the bifurcation of periodic solution, and the sufficient conditions for the existence and stability of semi-trivlal periodic solution and positive period-1 solution were obtained. The qualitative analysis and numerical results show that a positive period-1 solution bifurcates from the semi-trivial periodic solution through a fold bifurcation, a positive period-2 solution bifurcates from the positive period-1 solution through a flip bifurcation, and the chaotic solution is generated via a cascade of flip bifurcations. The superiority of the state feedback control strategy was also discussed.

关 键 词：脉冲动力系统 状态反馈控制 分岔 周期解 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程] O141[自动化与计算机技术—控制科学与工程]