\lambda update math in PID Lagrangian

[xujinming01]

The docstring in pid_update() shows that the PID controller update the lagrangian multiplier following the next equation:
$\lambda_{t+1} = \lambda_t + (K_p e_p + K_i \int e_p dt + K_d \frac{d e_p}{d t}) \eta$
But I cannot find the \eta in the method, and I don't find where to set it in the cfg.yaml
I think the math should be:
$\lambda_{t+1} = K_p e_p + K_i \int e_p dt + K_d \frac{d e_p}{d t}$
like the original paper:

I am very much looking forward to your reply.

[Gaiejj]

Thanks for your mentioning. Yes, the learning rate $\eta$ mentioned in the document does not have a corresponding interface; this is simply a more generalized expression. Our code implementation is consistent with the original formula provided.

We will make the documentation more precise in future updates.