An Unknown Input Multi-Observer Approach for Estimation, Attack Isolation, and Control of LTI Systems under Actuator Attacks

Abstract

We address the problem of state estimation, attack isolation, and control of discrete-time linear time-invariant systems under (potentially unbounded) actuator and sensor false data injection attacks. Using a bank of unknown input observers, each observer leading to an exponentially stable estimation error (in the attack-free case), we propose an observer-based estimator that provides exponential estimates of the system state in spite of actuator and sensor attacks. Exploiting sensor and actuator redundancy, the estimation scheme is guaranteed to work if a sufficiently small subset of sensors and actuators are under attack. Using the proposed estimator, we provide tools for reconstructing and isolating actuator and sensor attacks; and a control scheme capable of stabilizing the closed-loop dynamics by switching off isolated actuators. Simulation results are presented to illustrate the performance of our tools.Index Terms-Unknown input observers, cyber-physical systems, sensor and actuator attacks, linear systems, control.

Bank of Models: Sensor Attack Detection and Isolation in Industrial Control Systems

“…These works capture the process dynamics in the form of system models and use the point change detection methods to detect attacks in the process data. A similar recent approach [47] does isolate the attack but only the attacks on the actuators. Sensor fusion [34] and multi observer techniques [43] are recent efforts on attack isolation problem in simulated environments.…”

“…The Attack Isolation Problem: The attack isolation problem also known as determining the source of an attack is important in the context of ICS [47]. Anomaly detection research suffers from this issue, especially methods rooted in machine learning [41,2].…”

Kalman reduced form and pole placement by state feedback for multi‐input linear systems over Hermite rings

“…Finally, valuation rings like finite hyperreals 7 and power series algebras are also Hermite rings. Some regulation problems of cyber‐security systems 8 might be faced as regulation problems on linear systems with infinitesimal inputs, that is, over the ring of finite hyperreals, 9,10 or over some Krylov hyperreal space 11 . Classical reference for Hermite rings is Kaplansky's seminal work 12 .…”

“…Finally, our conclusions are given in Section 5. Special attention is payed to the regulator problem for linear systems with outputs 8,15 …”

“…Special attention is payed to the regulator problem for linear systems with outputs. 8,15 2 LINEAR SYSTEMS, POLE PLACEMENT, AND FEEDBACK ACTIONS Throughout this paper, all rings R will be commutative and with unit element 1. The characteristic polynomial det(zI−M) of a square matrix M ∈ R n×n is often denoted by 𝜒(M).…”