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I'm not sure if the Nyquist comment in the first answer applies to the kind of control you're talking about. Nyquist just says that you can reconstruct a signal if you are sampling at a rate that is twice the max frequency of interest. However, it says nothing about control bandwidth. From digital control theory, we know that the sampling rate will definitely affect your controller stability. However, actuator bandwidth as well as the dynamics in question will define what rate you'd have to control at and I don't think the answer can be clearly defined as a minimum of twice the frequency of interest. One thing that is similar is that as in reconstructing signals, the faster you can update your control the less instability will be introduced due to discrete sampling.

You also asked if you could run faster than 1 kHz and the answer is most definitely. Lots of low-level controllers run at up to 5 kHz or faster. If you are asking if that can be done reliably (hard real time) with ROS the answer is probably not unless you are using 3rd party libraries like orocos.