  This paper considers the distributed sparse identification problem over
wireless sensor networks such that all sensors cooperatively estimate the
unknown sparse parameter vector of stochastic dynamic systems by using the
local information from neighbors. A distributed sparse least squares algorithm
is proposed by minimizing a local information criterion formulated as a linear
combination of accumulative local estimation error and L_1-regularization term.
The upper bounds of the estimation error and the regret of the adaptive
predictor of the proposed algorithm are presented. Furthermore, by designing a
suitable adaptive weighting coefficient based on the local observation data,
the set convergence of zero elements with a finite number of observations is
obtained under a cooperative non-persistent excitation condition. It is shown
that the proposed distributed algorithm can work well in a cooperative way even
though none of the individual sensors can fulfill the estimation task. Our
theoretical results are obtained without relying on the independency
assumptions of regression signals that have been commonly used in the existing
literature. Thus, our results are expected to be applied to stochastic feedback
systems. Finally, the numerical simulations are provided to demonstrate the
effectiveness of our theoretical results.
