I’m reading a very informative paper. But I met some formulations hard to understand.
In assumption 2, they have the inequality of one step difference,
$$\Delta u_k \leq \sigma(B_o^{-1})\big(L_a\Delta u_{k-1}+L_a\Delta \zeta_k + m\Delta \dot{v}_{r,k}+\lambda_{\max}(K_v)\Delta s_k+\Delta\tau_{d,k}\big)$$
where $\Delta (\cdot)_k=\|(\cdot)_k-(\cdot)_{k-1}\|$ denotes one step difference; and $\zeta$, $\dot{v}$, $s$ are variables for the drone position, and $\tau$ for the attitude respectively.
The state they can safely neglect $\Delta\zeta$, $\Delta\dot{v}$, $\Delta s$ since the rate of the attitude control is much higher than that of the position control.
This part is hard to understand. What they focus is whether the drone positioning can safely be done using a machine learning and thus this ignoring seems to assume that the positioning system is already stable (a circle reasoning).
Or do I take the context wrong? Please help me understand how it is OK to safely neglect one-step difference of the position variables.
*FYI, I asked them this question directly 2 month ago (plus the reminder 2 weeks ago) and I do not have the reply yet.