Data-Driven Sparse System Identification
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In this paper, we study the system identification porblem for sparse linear time-invariant systems. We propose a sparsity promoting Lasso-type estimator to identify the dynamics of the system with only a limited number of input-state data samples. Using contemporary results on high-dimensional statistics, we prove that Ω(k_(m+n)) data samples are enough to reliably estimate the system dynamics, where n and m are the number of states and inputs, respectively, and k_ is the maximum number of nonzero elements in the rows of input and state matrices. The number of samples in the developed estimator is significantly smaller than the dimension of the problem for sparse systems, and yet it offers a small estimation error entry-wise. Furthermore, we show that, unlike the recently celebrated least-squares estimators for system identification problems, the method developed in this work is capable of exact recovery of the underlying sparsity structure of the system with the aforementioned number of data samples. Extensive case studies on synthetically generated systems and physical mass-spring networks are offered to demonstrate the effectiveness of the proposed method.
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