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\begin{description}
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\item[Mass-spring system] \marginnote{Mass-spring system}
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System of $N$ masses where each mass $i$ has a position $x_i \in \mathbb{R}$ and is connected through a sprint to mass $i-1$ and $i+1$. Each spring has an elastic constant $a_{j, i} = a_{i, j} > 0$.
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System of $N$ masses where each mass $i$ has a position $x_i \in \mathbb{R}$ and is connected through a spring to mass $i-1$ and $i+1$. Each spring has an elastic constant $a_{j, i} = a_{i, j} > 0$.
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\begin{figure}[H]
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\centering
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\begin{description}
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\item[Distributed gradient algorithm] \marginnote{Distributed gradient algorithm}
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Method that estimates a (more precise) set of parameters as a weighted sum those of its neighbors' (self-loop included):
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Method that estimates a (more precise) set of parameters as a weighted sum of those of its neighbors' (self-loop included):
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\[
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\vec{v}_i^{k+1} = \sum_{j \in \mathcal{N}_i} a_{ij} \z_j^k
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\]
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\]
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with $\x(t) \in \mathbb{R}^n$, $\u(t) \in U \subseteq \mathbb{R}^m$, $f(\x(t)) \in \mathbb{R}^n$, and $g(\x(t)) \in \mathbb{R}^{n \times m}$.
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$f(\x(t))$ can be seen as the drift of the system and $\u(t)$ a coefficient that controls how much $g(\x(t))$ is injected into $f(\x(t))$.
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$f(\x(t))$ can be seen as the drift of the system and $\u(t)$ as a coefficient that controls how much $g(\x(t))$ is injected into $f(\x(t))$.
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The overall system can be interpreted as composed of:
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\begin{itemize}
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