【摘要】 基于开闭环控制的思想,设计了一类由外激力与线性误差反馈组成的开闭环控制器,研究了Mathieu-Duffing振子混沌轨道至任意目标周期轨道的控制问题;同时,利用Liapunov稳定性理论与二阶常微分方程初值问题的一个比较定理,证明了上述开闭环控制夹带盆(basin of entrainment)的全局性.最后,利用数值模拟,验证了理论结果的正确性.更多还原

【Abstract】 Utilizing the idea of the open-plus-closed-loop(OPCL) control,a controller which is composed of an external excitation and linear feedback was designed to entrain the chaotic trajectories of Mathieu-Duffing oscillator to its periodic and higher periodic orbits.The global basin of entrainment of the open-plus-closed-loop control was proved by combining Liapunov stability theory with a comparative theorem of initial value problems for second-order ordinary differential equations.Numerical simulations were performed to demonstrate the theoretical results.更多还原