  We propose a distributed data-based predictive control scheme to stabilize a
network system described by linear dynamics. Agents cooperate to predict the
future system evolution without knowledge of the dynamics, relying instead on
learning a data-based representation from a single sample trajectory. We employ
this representation to reformulate the finite-horizon Linear Quadratic
Regulator problem as a network optimization with separable objective functions
and locally expressible constraints. We show that the controller resulting from
approximately solving this problem using a distributed optimization algorithm
in a receding horizon manner is stabilizing. We validate our results through
numerical simulations.
