Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Data-driven stabilization of unknown linear-threshold network dynamics
X. Wang, D. Duong-Tran, J. Cortés
IEEE Transactions on Automatic Control, submitted
Abstract
This paper studies the data-driven control of
unknown linear-threshold network dynamics to
stabilize the state to a reference value. We
consider two types of controllers: (i) a state
feedback controller with feed-forward reference
input and (ii) an augmented feedback controller with
error integration. The first controller features a
simpler structure and is easier to design, while the
second offers improved performance in the presence
of system parameter changes and disturbances. Our
design strategy employs state-input datasets to
construct data- based representations of the
closed-loop dynamics. Since these representations
involve linear threshold functions, we rewrite them
as switched linear systems, and formulate the design
prob- lem as that of finding a common controller for
all the resulting modes. This gives rise to a set of
linear matrix inequalities (LMIs) whose solutions
corresponds to the controller gain matrices. We
analyze the computational complexity of solving the
LMIs and propose a simplified, sufficient set of
conditions that scales linearly with the system
state. Simulations on two case studies involving
regulation of firing rate dynamics in rodent brains
and of arousal level dynamics in humans demonstrate
the effectiveness of the controller designs.
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Mechanical and Aerospace Engineering,
University of California, San Diego
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Ph: 1-858-822-7930
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cortes at ucsd.edu
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jorgilliyo