# Securing State Estimation Under Sensor and Actuator Attacks: Theory and Design

## TL;DR

This paper introduces a new condition called sparse strong observability for secure state estimation in linear systems under arbitrary sensor and actuator attacks, and proposes a scalable estimator based on satisfiability modulo theory solving.

## Contribution

It defines sparse strong observability as a necessary and sufficient condition for attack-resilient state reconstruction and develops a novel estimator leveraging satisfiability modulo theory solving.

## Key findings

- The proposed estimator effectively reconstructs states under adversarial attacks.
- Sparse strong observability is essential for secure state estimation.
- Numerical simulations show the estimator's effectiveness and scalability.

## Abstract

This paper discusses the problem of estimating the state of a linear time-invariant system when some of its sensors and actuators are compromised by an adversarial agent. In the model considered in this paper, the malicious agent attacks an input (output) by manipulating its value arbitrarily, i.e., we impose no constraints (statistical or otherwise) on how control commands (sensor measurements) are changed by the adversary. In the first part of this paper, we introduce the notion of sparse strong observability and we show that is a necessary and sufficient condition for correctly reconstructing the state despite the considered attacks. In the second half of this work, we propose an estimator to harness the complexity of this intrinsically combinatorial problem, by leveraging satisfiability modulo theory solving. Numerical simulations demonstrate the effectiveness and scalability of our estimator.