更快地控制混沌
Controlling Chaos Faster
摘要：
预测反馈控制是一种易于实现的混沌动力系统稳定未知不稳定周期轨道的方法。预测反馈控制受到严重限制，因为渐近收敛速度随着较强的不稳定性而降低，这反过来又是较大目标周期的典型情况，使得难以有效地稳定大周期的周期轨道。在这里，我们研究停滞的混沌控制，控制的应用是停滞，利用混沌，不受控制的动态，并引入一个自适应范式，以克服这一限制，加快收敛。理论和应用结果表明，改进的预测反馈控制不仅能稳定更多的周期轨道，而且能加快典型混沌映射的收敛速度。所提出的自适应方案提供了一种在线调整参数的方法，从而产生一种广泛适用的快速混沌控制，即使对于大周期的周期轨道也能可靠地收敛。
英文摘要：
Predictive Feedback Control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive Feedback Control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we study stalled chaos control, where the application of control is stalled to make use of the chaotic, uncontrolled dynamics, and introduce an adaptation paradigm to overcome this limitation and speed up convergence. This modified control scheme is not only capable of stabilizing more periodic orbits than the original Predictive Feedback Control but also speeds up convergence for typical chaotic maps, as illustrated in both theory and application. The proposed adaptation scheme provides a way to tune parameters online, yielding a broadly applicable, fast chaos control that converges reliably, even for periodic orbits of large period.
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