DeepAI AI Chat
Log In Sign Up

Data-Driven Sparse System Identification

by   Salar Fattahi, et al.
berkeley college

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.


page 1

page 2

page 3

page 4


Learning Sparse Dynamical Systems from a Single Sample Trajectory

This paper addresses the problem of identifying sparse linear time-invar...

Predicting sparse circle maps from their dynamics

The problem of identifying a dynamical system from its dynamics is of gr...

On Identification of Sparse Multivariable ARX Model: A Sparse Bayesian Learning Approach

This paper begins with considering the identification of sparse linear t...

Identification of linear time-invariant systems with Dynamic Mode Decomposition

Dynamic mode decomposition (DMD) is a popular data-driven framework to e...

Exact Recovery for System Identification with More Corrupt Data than Clean Data

In this paper, we study the system identification problem for linear dis...

Learning the Structure of Large Networked Systems Obeying Conservation Laws

Many networked systems such as electric networks, the brain, and social ...

Surrogate Aided Unsupervised Recovery of Sparse Signals in Single Index Models for Binary Outcomes

We consider the recovery of regression coefficients, denoted by β_0, for...