Centre for Applied Dynamics Research, School of Engineering, King's College, University of Aberdeen, Aberdeen, UK.
Philos Trans A Math Phys Eng Sci. 2013 May 20;371(1993):20120428. doi: 10.1098/rsta.2012.0428. Print 2013 Jun 28.
This paper proposes a new control method applicable for a class of non-autonomous dynamical systems that naturally exhibit coexisting attractors. The central idea is based on knowledge of a system's basins of attraction, with control actions being applied intermittently in the time domain when the actual trajectory satisfies a proximity constraint with regards to the desired trajectory. This intermittent control uses an impulsive force to perturb one of the system attractors in order to switch the system response onto another attractor. This is carried out by bringing the perturbed state into the desired basin of attraction. The method has been applied to control both smooth and non-smooth systems, with the Duffing and impact oscillators used as examples. The strength of the intermittent control force is also considered, and a constrained intermittent control law is introduced to investigate the effect of limited control force on the efficiency of the controller. It is shown that increasing the duration of the control action and/or the number of control actuations allows one to successfully switch between the stable attractors using a lower control force. Numerical and experimental results are presented to demonstrate the effectiveness of the proposed method.
本文提出了一种适用于一类非自治动力系统的新控制方法，这类系统自然表现出共存吸引子。该方法的核心思想基于对系统吸引域的了解，当实际轨迹与期望轨迹满足接近约束时，控制作用会在时域中间歇性地施加。这种间歇性控制使用脉冲力来扰动系统的一个吸引子，从而将系统响应切换到另一个吸引子上。通过将受扰状态带入期望的吸引域来实现这一点。该方法已应用于控制平滑和非平滑系统，其中使用了 Duffing 和冲击振荡器作为示例。还考虑了间歇性控制力的强度，并引入了约束间歇性控制律来研究有限控制力对控制器效率的影响。结果表明，通过增加控制作用的持续时间和/或控制作用的次数，可以使用较低的控制力在稳定吸引子之间成功切换。本文还提出了数值和实验结果，以证明所提出方法的有效性。
