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

Vito Cerone, Sophie M. Fosson, Diego Regruto, Francesco Ripa

TL;DR

This work addresses secure state estimation for discrete-time LTI CPS under sparse sensor attacks by formulating a Lasso-based SSE problem that estimates both the delayed state and attack support via an unconstrained objective. It further derives an online, ISTA-derived sparse observer that enables recursive SSE in real time. A tailored irrepresentable-condition analysis provides guidance on when attack-support recovery is guaranteed, and a recursive sparse observer extends the approach to streaming data. Numerical results show competitive accuracy and substantially lower computation time compared with state-of-the-art methods, highlighting the method's practicality for real-time CPS security.

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.

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

TL;DR

This work addresses secure state estimation for discrete-time LTI CPS under sparse sensor attacks by formulating a Lasso-based SSE problem that estimates both the delayed state and attack support via an unconstrained objective. It further derives an online, ISTA-derived sparse observer that enables recursive SSE in real time. A tailored irrepresentable-condition analysis provides guidance on when attack-support recovery is guaranteed, and a recursive sparse observer extends the approach to streaming data. Numerical results show competitive accuracy and substantially lower computation time compared with state-of-the-art methods, highlighting the method's practicality for real-time CPS security.

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.
Paper Structure (9 sections, 1 theorem, 20 equations, 4 figures, 1 algorithm)

This paper contains 9 sections, 1 theorem, 20 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Lasso approach
  4. Analysis of the irrepresentable condition
  5. Sparse soft observer for online SSE
  6. Numerical results
  7. Lasso approach
  8. Sparse soft observer
  9. Conclusions

Key Result

Theorem 1

Let us assume that $\in\mathbb{R}^{p\tau,n+h}$ is full rank. Lasso is successful, i.e., by solving it we identify the attack support, if and only if provided that $\lambda>0$ is sufficiently small. As a consequence, Lasso is successful if

Figures (4)

  • Figure 1: Lasso vs ETPG vs Imhotep-SMT, $n=20$, $s=p/5$, noise-free and with noise bound $10^{-4}$
  • Figure 2: Lasso vs ETPG vs Imhotep-SMT, $n=20$, $p=30$, noise-free and with noise bound $10^{-4}$
  • Figure 3: Sparse soft observer vs ETPL; $n=10$, $p=15$, $s=3$, $\tau=n$
  • Figure 4: Sparse soft observer vs ETPL; $n=10$, $p=15$, $s=3$, $\tau=1$

Theorems & Definitions (3)

  • Theorem 1
  • proof
  • Example 1