Chang Austin, Bienfang Joshua C., Hall G. Martin, Gardner Jeff R., Gauthier Daniel J.
Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Box 90305, Durham, North Carolina 27708.
Chaos. 1998 Dec;8(4):782-790. doi: 10.1063/1.166357.
We describe a method for stabilizing unstable steady states in nonlinear dynamical systems using a form of extended time-delay autosynchronization. Specifically, stabilization is achieved by applying a feedback signal generated by high-pass-filtering in real time the dynamical state of the system to an accessible system parameter or variables. Our technique is easy to implement, does not require knowledge of the unstable steady state coordinates in phase space, automatically tracks changes in the system parameters, and is more robust to broadband noise than previous schemes. We demonstrate the controller's efficacy by stabilizing unstable steady states in an electronic circuit exhibiting low-dimensional temporal chaos. The simplicity and robustness of the scheme suggests that it is ideally suited for stabilizing unstable steady states in ultra-high-speed systems. (c) 1998 American Institute of Physics.
我们描述了一种使用扩展时间延迟自同步形式来稳定非线性动力系统中不稳定稳态的方法。具体而言，通过将对系统动态状态进行实时高通滤波所生成的反馈信号应用于一个可访问的系统参数或变量来实现稳定。我们的技术易于实现，不需要知道相空间中不稳定稳态的坐标，能自动跟踪系统参数的变化，并且比以前的方案对宽带噪声更具鲁棒性。我们通过在一个呈现低维时间混沌的电子电路中稳定不稳定稳态来证明控制器的有效性。该方案的简单性和鲁棒性表明它非常适合用于稳定超高速系统中的不稳定稳态。（c）1998美国物理研究所。
