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Fix typo <noupdate>

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This commit is contained in:
Tian Cheng (Riccardo) Xia
2025-06-10 17:17:15 +02:00
parent 067db624fb
commit 7baa556800
1 changed files with 2 additions and 2 deletions
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4
src/year2/distributed-autonomous-systems/sections/_safety_controllers.tex
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@ -191,7 +191,7 @@
- &\gamma(V_{ij}^{s}(\x_i, \x_j)) \leq 0 \\
&\forall j \in \mathcal{N}_i, \forall i \in \{1, \dots, N\} \Big\}
\end{aligned} \\
= \Big\{ \u \in \mathbb{R}^{dN} \mid -2(\x_i, \x_j)^T \u_i - 2(\x_j-\x_i)^T \u_j - \gamma(V_{ij}^s(\x_i, \x_j)) \leq 0 \,\,\forall j \in \mathcal{N}_i, \forall i \in \{1, \dots, N\} \Big\}
= \Big\{ \u \in \mathbb{R}^{dN} \mid -2(\x_i-\x_j)^T \u_i - 2(\x_j-\x_i)^T \u_j - \gamma(V_{ij}^s(\x_i, \x_j)) \leq 0 \,\,\forall j \in \mathcal{N}_i, \forall i \in \{1, \dots, N\} \Big\}
\end{aligned}
\]
@ -208,7 +208,7 @@
\arg\min_{\u \in \mathbb{R}^N} \sum_{i=1}^{N} \Vert \u_i - \u_i^\text{ref} \Vert^2 \\
\begin{aligned}
\text{subject to }
&-2(\x_i, \x_j)^T \u_i - 2(\x_j-\x_i)^T \u_j - \gamma(V_{ij}^s(\x_i, \x_j)) \leq 0 \\
&-2(\x_i-\x_j)^T \u_i - 2(\x_j-\x_i)^T \u_j - \gamma(V_{ij}^s(\x_i, \x_j)) \leq 0 \\
& \Vert \u_i \Vert \leq \u_i^\text{max} \\
& \forall j \in \mathcal{N}_i, \forall i \in \{ 1, \dots, N \}
\end{aligned}