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Fix typos <noupdate>

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Tian Cheng (Riccardo) Xia
2025-05-25 14:15:20 +02:00
parent fdcbfa6e4a
commit 7545b870c9
2 changed files with 4 additions and 4 deletions
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src/year2/distributed-autonomous-systems/sections/_feedback_optimization.tex
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@ -173,7 +173,7 @@
Use $\x_i$ to approximate $h_i(\u_i)$ and dynamic average consensus for the aggregation function. The dynamics is: Use $\x_i$ to approximate $h_i(\u_i)$ and dynamic average consensus for the aggregation function. The dynamics is:
\[ \[
\begin{split} \begin{split}
\dot{\u}_i &= -\delta_1 \nabla h_i(\u_i) \left( \nabla_{[\x_i]} l_i(\x_i, \phi_i(\x_i)+\w_i) + \left( \nabla_{[\phi_i(\x_i)+\w_i]} l_i(\x_i, \phi_i(\x_i)+\w_i) + \v_i \right) \nabla \phi_i(\x_i) \right) \\ \dot{\u}_i &= -\delta_1 \nabla h_i(\u_i) \Big( \nabla_{[\x_i]} l_i(\x_i, \phi_i(\x_i)+\w_i) + \left( \nabla_{[\phi_i(\x_i)+\w_i]} l_i(\x_i, \phi_i(\x_i)+\w_i) + \v_i \right) \nabla \phi_i(\x_i) \Big) \\
\delta_2 \dot{\w}_i &= - \sum_{j \in \mathcal{N}_i} a_{ij} (\w_i - \w_j) - \sum_{j \in \mathcal{N}_i} a_{ij} (\phi_i(\x_i) - \phi_i(\x_j)) \\ \delta_2 \dot{\w}_i &= - \sum_{j \in \mathcal{N}_i} a_{ij} (\w_i - \w_j) - \sum_{j \in \mathcal{N}_i} a_{ij} (\phi_i(\x_i) - \phi_i(\x_j)) \\
\delta_2 \dot{\v}_i &= - \sum_{j \in \mathcal{N}_i} a_{ij} (\v_i - \v_j) - \sum_{j \in \mathcal{N}_i} a_{ij} (\nabla_{[\phi_i(\x_i)+\w_i]} l_i(\x_i, \phi_i(\x_i)+\w_i) - \nabla_{[\phi_j(\x_j)+\w_j]} l_j(\x_j, \phi_j(\x_j)+\w_j)) \\ \delta_2 \dot{\v}_i &= - \sum_{j \in \mathcal{N}_i} a_{ij} (\v_i - \v_j) - \sum_{j \in \mathcal{N}_i} a_{ij} (\nabla_{[\phi_i(\x_i)+\w_i]} l_i(\x_i, \phi_i(\x_i)+\w_i) - \nabla_{[\phi_j(\x_j)+\w_j]} l_j(\x_j, \phi_j(\x_j)+\w_j)) \\
\end{split} \end{split}

6
src/year2/distributed-autonomous-systems/sections/_safety_controllers.tex
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@ -217,7 +217,7 @@
where $\u_i^\text{ref}$ is the reference input of the high level controller and $\u_i^\text{max}$ is the bound. where $\u_i^\text{ref}$ is the reference input of the high level controller and $\u_i^\text{max}$ is the bound.
\begin{remark} \begin{remark}
The policy should be computed continuously for each $x_i(t)$. The policy should be computed continuously for each $\x_i(t)$.
\end{remark} \end{remark}
\item[Decentralized safety controller] \marginnote{Decentralized safety controller} \item[Decentralized safety controller] \marginnote{Decentralized safety controller}
@ -255,13 +255,13 @@
\begin{split} \begin{split}
\dot{\vec{p}}_x &= v \cos(\theta) \\ \dot{\vec{p}}_x &= v \cos(\theta) \\
\dot{\vec{p}}_y &= v \sin(\theta) \\ \dot{\vec{p}}_y &= v \sin(\theta) \\
\theta &= \omega \\ \dot{\theta} &= \omega \\
\end{split} \end{split}
\] \]
where: where:
\begin{itemize} \begin{itemize}
\item $(\vec{p}_x, \vec{p}_y)$ is the position of the center of mass, \item $(\vec{p}_x, \vec{p}_y)$ is the position of the center of mass,
\item $\theta$ is the orientation, \item $\dot{\theta}$ is the orientation,
\item $v$ is the linear velocity, \item $v$ is the linear velocity,
\item $\omega$ is the angular velocity. \item $\omega$ is the angular velocity.
\end{itemize} \end{itemize}