Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Data-driven control of linear-threshold network dynamics
X. Wang, J. Cortés
American Control Conference, Atlanta, Georgia, 2022, pp. 114-119
Abstract
This paper studies the data-driven stabilization of
linear-threshold network models. Our goal is to design a
linear state feedback controller to stabilize the system
to the origin purely based on data samples, instead of a
parametric model. To achieve this, we first establish a
data-based representation for the linear-threshold
network in an open-loop form. This is done by
introducing a map that represents the state-input pair
as a transformation of data matrices. We then employ a
linear feedback controller in the formulation of the map
and obtain a closed-loop data-based representation for
the system. To facilitate the design of the feedback
gain matrix, we rewrite the dynamics as a switched
linear system relying on the special structure of linear
thresholding. The design problem then becomes equivalent
to solving a system of linear matrix inequalities
(LMIs). We analyze the associated computational
complexity and, to reduce it, we introduce a different
set of LMIs that act as a sufficient condition to obtain
the linear control design. Simulations demonstrate the
effectiveness of the proposed approach.
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Mechanical and Aerospace Engineering,
University of California, San Diego
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