A Robust Circle-criterion Observer-based Estimator for Discrete-time Nonlinear Systems in the Presence of Sensor Attacks

Abstract

We address the problem of robust state estimation and attack isolation for a class of discrete-time nonlinear systems with positive-slope nonlinearities under (potentially unbounded) sensor attacks and measurement noise. We consider the case when a subset of sensors is subject to additive false data injection attacks. Using a bank of circle-criterion observers, each observer leading to an Input-to-State Stable (ISS) estimation error, we propose a estimator that provides robust estimates of the system state in spite of sensor attacks and measurement noise; and an algorithm for detecting and isolating sensor attacks. Our results make use of the ISS property of the observers to check whether the trajectories of observers are consistent with the attack-free trajectories of the system. Simulations results are presented to illustrate the performance of the results.

A Secure Sensor Fusion Framework for Connected and Automated Vehicles under Sensor Attacks

“…Remark 1 It is usually assumed in the literature, e.g., [10], [7], [12], [11], [28], [29], [31] that the set of attacked nodes is time-invariant, i.e., the attacker cannot change his mind by attacking the other nodes rather than the ones he chose initially. We relax this assumption by allowing the set of attacked sensors to be time-varying, i.e., the attacker can choose a different set of sensors to compromise at different time.…”

“…Sensor redundancy has been proved to be crucial for estimation under attacks [27], [10], [28], [29], [14], [30]. Using redundant sensors/actuators for secure estimation and control is a commonly adopted technique, see, e.g., [27], [10], [28], [29], [11], [31], and references therein. Note that it might be costly to create redundancy, which indicates some of these estimation methods might have conservative applications; however, for security-critical systems, for instance, CAVs, this is the price to pay [6].…”

Joint Parameter and State Estimation of Noisy Discrete-Time Nonlinear Systems: A Supervisory Multi-Observer Approach

“…p−p N , where p and p denote the extrema of the set that is currently being sampled (for the dynamic scheme p and p will move closer together over time). For this sampling scheme, we can guarantee (17) with ρ(∆ m , N ) = ∆m N , as the distance between the true parameter and the nearest sample never exceeds half the distance between neighbouring samples. This also guarantees (3) for the static sampling since ρ(∆ 0 , N ) → 0 as N → ∞.…”

“…Define ν := min{ν p, 1 3 γ −1 p (ν x)}, consider the K ∞functions χ, χp , χv , χw from Lemma 2 and let ∆ ∈ (0, ∆ 0 ) be sufficiently small such that 3 χp (ρ( ∆, 0)) < χ(ν) χ(ν p), which is always possible since χ, χp ∈ K ∞ and since ρ is the KL-function in (17). Choose ǫ ∈ (0, 1 3 χ(α ∆)) sufficiently small such that…”

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

“…In [15], Satisfiability Modulo Theory (SMT) solvers are used for state estimation for nonlinear differentially flat systems with corrupted sensors. In our previous work [16], [17], the problem of state estimation and attack isolation for a class of nonlinear systems with positive-slope nonlinearities is considered. Similar to the ideas given in [18], we provided an observer-based estimation/isolation strategy, using a bank of circle-criterion observers, which provides a robust estimate of the system state in spite of sensor attacks and effectively pinpoints attacked sensors.…”