LQG Reference Tracking with Safety and Reachability Guarantees under Unknown False Data Injection Attacks

TL;DR

This paper develops a control strategy for LQG tracking that guarantees safety and reachability despite unknown false data injection attacks, using a QCQP-based policy and barrier certificates.

Contribution

It introduces a novel control policy that ensures safety and reachability under sensor attacks by considering multiple sensor compromise scenarios and employing barrier certificates.

Findings

Achieves desired safety and reachability probabilities.

Effective control policy under unknown sensor attacks.

Validated through numerical case study.

Abstract

We investigate a linear quadratic Gaussian (LQG) tracking problem with safety and reachability constraints in the presence of an adversary who mounts an FDI attack on an unknown set of sensors. For each possible set of compromised sensors, we maintain a state estimator disregarding the sensors in that set, and calculate the optimal LQG control input at each time based on this estimate. We propose a control policy which constrains the control input to lie within a fixed distance of the optimal control input corresponding to each state estimate. The control input is obtained at each time step by solving a quadratically constrained quadratic program (QCQP). We prove that our policy can achieve a desired probability of safety and reachability using the barrier certificate method. Our control policy is evaluated via a numerical case study.