Abstract

Motivated by the need to secure cyber-physical systems against attacks, we consider the problem of estimating the state of a noisy linear dynamical system when a subset of sensors is arbitrarily corrupted by an adversary. We propose a secure state estimation algorithm and derive (optimal) bounds on the achievable state estimation error. In addition, as a result of independent interest, we give a coding theoretic interpretation for prior work on secure state estimation against sensor attacks in a noiseless dynamical system.

Highlights

  • Cyber-physical systems (CPS) manage the vast majority of today’s critical infrastructure and securing such CPS against malicious attacks is a problem of growing importance [1]

  • As a stepping stone towards securing complex CPS deployed in practice, several recent works have studied security problems in the context of linear dynamical systems [1], [2], [3], [4], [5], [6] leading to a fundamental understanding of how the system dynamics can be leveraged for security guarantees

  • In this paper we focus on securely estimating the state of a linear dynamical system from a set of noisy and maliciously corrupted sensor measurements

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Summary

INTRODUCTION

Cyber-physical systems (CPS) manage the vast majority of today’s critical infrastructure and securing such CPS against malicious attacks is a problem of growing importance [1]. As a stepping stone towards securing complex CPS deployed in practice, several recent works have studied security problems in the context of linear dynamical systems [1], [2], [3], [4], [5], [6] leading to a fundamental understanding of how the system dynamics can be leveraged for security guarantees With this motivation, in this paper we focus on securely estimating the state of a linear dynamical system from a set of noisy and maliciously corrupted sensor measurements. In contrast to prior work in the Gaussian noise setup, we consider a general linear dynamical system and give (optimal) guarantees on the achievable state estimation error against arbitrary sensor attacks.

System model
State estimation: prediction and filtering
Causal knowledge assumptions
Sparse observability condition
MAIN RESULTS
SECURE STATE ESTIMATION
SPARSE OBSERVABILITY
Algorithm 2: performance analysis
Bounds on the trace of product of symmetric matrices
Secure state filtering
Full Text
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