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...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.展开更多
By using the idea of open-plus-closed-loop（OPCL） control, a controller composed of an external excitation and a linear feedback is designed to entrain chaotic trajectories of Mathieu-Duffing oscillator to its period...By using the idea of open-plus-closed-loop（OPCL） control, a controller composed of an external excitation and a linear feedback is designed to entrain chaotic trajectories of Mathieu-Duffing oscillator to its periodic and higher periodic orbits. The global basin of entrainment of this open-plus-closed-loop control is proved by combining the Lyapunov stability theory with a comparative theorem of initial value problems for second-order ordinary differential equations. Numerical simulations are performed to verify the theoretical results.展开更多
文摘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.
基金Project supported by the National Natural Science Foundation of China (No. 10672193)
文摘By using the idea of open-plus-closed-loop（OPCL） control, a controller composed of an external excitation and a linear feedback is designed to entrain chaotic trajectories of Mathieu-Duffing oscillator to its periodic and higher periodic orbits. The global basin of entrainment of this open-plus-closed-loop control is proved by combining the Lyapunov stability theory with a comparative theorem of initial value problems for second-order ordinary differential equations. Numerical simulations are performed to verify the theoretical results.
