Title:
From Global, Finite-Time, Linear Computations to Local, Edge-Based Interaction Rules
From Global, Finite-Time, Linear Computations to Local, Edge-Based Interaction Rules
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Author(s)
Costello, Zak
Egerstedt, Magnus B.
Egerstedt, Magnus B.
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Abstract
A network of locally interacting agents can be
thought of as performing a distributed computation. But not
all computations can be faithfully distributed. This paper investigates
which global, linear transformations can be computed
in finite time using local rules with time varying weights, i.e.,
rules which rely solely on information from adjacent nodes in
a network. The main result states that a linear transformation
is computable in finite time using local rules if and only if the
transformation has positive determinant. An optimal control
problem is solved for finding the local interaction rules, and
simulations are performed to elucidate how optimal solutions
can be obtained.
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Date Issued
2015-08
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Article