Lasso-based state estimation for cyber-physical systems under sensor attacks

TL;DR

This paper introduces a Lasso-based method for secure state estimation in cyber-physical systems under sensor attacks, providing theoretical guarantees and an online estimation approach, with promising numerical results.

Contribution

It proposes a novel Lasso-based approach for attack detection and state estimation, with theoretical analysis and an online sparse state observer.

Findings

Theoretical conditions guarantee successful attack and state recovery.

The Lasso-based method performs comparably or better than existing algorithms.

An online sparse state observer is developed for real-time estimation.

Abstract

The development of algorithms for secure state estimation in vulnerable cyber-physical systems has been gaining attention in the last years. A consolidated assumption is that an adversary can tamper a relatively small number of sensors. In the literature, block-sparsity methods exploit this prior information to recover the attack locations and the state of the system. In this paper, we propose an alternative, Lasso-based approach and we analyse its effectiveness. In particular, we theoretically derive conditions that guarantee successful attack/state recovery, independently of established time sparsity patterns. Furthermore, we develop a sparse state observer, by starting from the iterative soft thresholding algorithm for Lasso, to perform online estimation. Through several numerical experiments, we compare the proposed methods to the state-of-the-art algorithms.