Fully Distributed Resilient State Estimation Based on Distributed Median Solver

Abstract

In this paper, we present a scheme of fully distributed resilient state estimation for linear dynamical systems under sensor attacks. The proposed state observer consists of a network of local observers, where each of them utilizes local measurements and information transmitted from the neighbors. As a fully distributed scheme, it does not necessarily collect a majority of sensing data for the sake of attack identification, while the compromised sensors are eventually identified by the distributed network and excluded from the observers. For this, the overall network (not the individual local observer) is assumed to have redundant sensors and assumed to be connected. The proposed scheme is based on a novel design of a distributed median solver, which approximately recovers the median value of local estimates.

Distributed Dynamic Quantile Solver With Plug-and-Play Operation

“…Since ϵ ′′ depends explicitly on ρ, α, and γ, let T * ρ (α, γ) := T • (ϵ ′′ ) ≥ 0. Then, (19) holds for all t ≥ T * ρ (α, γ).…”

“…The intuition behind the distributed algorithm (2) comes from the blended dynamics approach introduced in [17]- [19]. In this approach, we consider the heterogeneous multiagent systems whose dynamics are given by…”

Decentralized Secure State-Tracking in Multi-Agent Systems

“…Moreover, they only solve a subset of the DSST problem since they make assumptions either on system dynamics, network, or both. For example, both [18] and [4] make assumptions on system dynamics. In particular, they require the existence of a basis such that the unobservable space of all the (or enough) sensors is the span of a subset of this basis.…”

“…Intrinsically, SD enables one to decompose a DSST problem into multiple sub-problems each associated with a scalar system. Interestingly, [18] and [4] exploit SD in different ways which leads to different types of solutions of the DSST problem. In [18], with the help of SD, the DSST problem is formulated as a distributed convex optimization problem with time-varying loss function and a high-gain observer is proposed to reconstruct the state with the help of "blended dynamics approach" introduced in [19].…”

“…Interestingly, [18] and [4] exploit SD in different ways which leads to different types of solutions of the DSST problem. In [18], with the help of SD, the DSST problem is formulated as a distributed convex optimization problem with time-varying loss function and a high-gain observer is proposed to reconstruct the state with the help of "blended dynamics approach" introduced in [19]. In contrast, [4] proposes a local filter which forces the estimate of an attack-free sensor to always lie in the convex hull of the estimates of its attack-free neighbors.…”