DPS系统的动力学分析与控制

对DPS系统进行了分析与控制,计算耗散性函数得到其耗散性,结合李雅普诺夫指数证明了其混沌性;根据Routh-Hurwitz判据判断了平衡点的稳定性,采用matlab数值模拟相图验证了该系统具有丰富的动力学现象且与Lorenz系统拓扑不相似;利用微分反馈控制法、恒外激励控制法和x|x|控制法分别对DPS系统进行了混沌控制,Matlab仿真实验验证了对DPS系统可有效控制;完善了x|x|控制法,并对Lorenz系统、Chen系统、Lu系统、Rossler系统进行控制并利用matlab进行数值仿真相图和分岔图。

Dynamic Analysis and Control of DPS System

In this paper, we analyze and control the DPS system, calculate the dissipation function, and prove its chaos with Lyapunov index. Routh-hurwitz criterion was used to judge the stability of the equilibrium point, and matlab numerical simulation phase diagram verified that the system has a rich dynamic phenomenon and is not similar to Lorenz system topology. Three methods, namely differential feedback control method, constant external excitation control method and x|x| control method, were used to control the chaos of the DPS system respectively. Matlab simulation shows that the DPS system can be effectively controlled. X |x| control method is improved, and Lorenz system, Chen system, Lu system, Rossler system control and matlab numerical simulation phase diagram and bifurcation diagram are obtained.