论文标题
评论“使用不断变化的时间延迟的延迟反馈控制算法的自适应修改” https://doi.org/10.1016/j.physleta.2011.08.072
Comment on "Adaptive modification of the delayed feedback control algorithm with a continuously varying time delay" https://doi.org/10.1016/j.physleta.2011.08.072
论文作者
论文摘要
在论文中https://doi.org/10.1016/j.physleta.2011.08.072作者提出了对常规延迟反馈控制算法的修改，其中时间延迟持续变化，以最大程度地减少控制力的能力。最小化是通过梯度散发法实现的。但是，相对于时间延迟的梯度的推导是不准确的。特别是，省略了标量因子。标量因子的绝对值并不重要，因为它仅改变梯度方法的速度。另一方面，因子的符号改变了梯度方向，因此对于乘数的负值，梯度定位成为梯度呈梯度的方法，而失败功率最小化。在此提出了梯度的精确推导。我们获得了缺失因子的分析表达，并显示了发生负因子的洛伦兹系统的示例。我们还讨论了该因素的负面性与奇数限制定理之间的关系。
In the paper https://doi.org/10.1016/j.physleta.2011.08.072 authors propose a modification of the conventional delayed feedback control algorithm, where time-delay is varied continuously to minimize the power of control force. Minimization is realized via gradient-descent method. However, the derivation of the gradient with respect to time-delay is not accurate. In particular, a scalar factor is omitted. The absolute value of the scalar factor is not crucial, as it only changes the speed of the gradient method. On the other hand, the factor's sign changes the gradient direction, therefore for negative value of the multiplier the gradient-decent becomes gradient-ascent method and fail power minimization. Here the accurate derivation of the gradient is presented. We obtain an analytical expression for the missing factor and show an example of the Lorenz system where the negative factor occurs. We also discuss a relation between the negativeness of the factor and the odd number limitation theorem.
