Jorge Cortés
Professor
Cymer Corporation Endowed Chair
On the minimum-energy control of neural populations
with rectified activation function
T. Menara, J. Cortés
Chaos, submitted
Abstract
Controlling neural assemblies is a key challenge in
both biological and artificial domains. The
derivation of prescriptive control methods may
inform the development of novel, targeted therapies,
and promote the development of the next generation
of machine learning algorithms. In this context, the
best control methods utilize the least amount of
energy to steer the network state to a desired
value. In this work, we utilize control-theoretic
tools to derive energy-efficient control strategies
for neural populations with rectified activation
function. We first show that any state in the
positive orthant is reachable in finite time. We
then provide energy metric estimates based on the
controllability Gramian matrix. In the case of
scalar systems (i.e., isolated neural populations),
we derive minimum-energy (optimal) control
strategies that are based on the combination of
simple control primitives - that is, simple
maneuvers such as holding the state or letting it
coast along the system's natural flow. We then
extend these control strategies to the particular
case of neural population pairs and finally to
purely inhibitory or excitatory networks of
arbitrary size. Numerical studies demonstrate that
our control strategies outperform naive feedback
controllers in terms of control energy.
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Mechanical and Aerospace Engineering,
University of California, San Diego
9500 Gilman Dr,
La Jolla, California, 92093-0411
Ph: 1-858-822-7930
Fax: 1-858-822-3107
cortes at ucsd.edu
Skype id:
jorgilliyo