Localization and Estimation of Unknown Forced Inputs: A Group LASSO Approach

TL;DR

This paper develops a probabilistic group LASSO-based method to localize sparse unknown inputs in linear dynamical systems, with applications to power grid oscillation detection, providing theoretical guarantees and empirical validation.

Contribution

It introduces a novel probabilistic analysis for group LASSO in dynamical systems, offering explicit bounds on localization accuracy and error, applicable to power networks.

Findings

Provided bounds on wrong source identification probability.

Achieved accurate input and state estimation in simulations.

Validated approach on IEEE power system model.

Abstract

We model and study the problem of localizing a set of sparse forcing inputs for linear dynamical systems from noisy measurements when the initial state is unknown. This problem is of particular relevance to detecting forced oscillations in electric power networks. We express measurements as an additive model comprising the initial state and inputs grouped over time, both expanded in terms of the basis functions (i.e., impulse response coefficients). Using this model, with probabilistic guarantees, we recover the locations and simultaneously estimate the initial state and forcing inputs using a variant of the group LASSO (linear absolute shrinkage and selection operator) method. Specifically, we provide a tight upper bound on: (i) the probability that the group LASSO estimator wrongly identifies the source locations, and (ii) the $\ell_2$-norm of the estimation error. Our bounds explicitly depend upon the length of the measurement horizon, the noise statistics, the number of inputs and sensors, and the singular values of impulse response matrices. Our theoretical analysis is one of the first to provide a complete treatment for the group LASSO estimator for linear dynamical systems under input-to-output delay assumptions. Finally, we validate our results on synthetic models and the IEEE 68-bus, 16-machine system.