Byzantine-Resilient Distributed Observers for LTI Systems

TL;DR

This paper develops a distributed state estimation algorithm for LTI systems that is resilient to Byzantine adversaries, using network robustness properties to guarantee correctness.

Contribution

It introduces a novel attack-resilient estimation algorithm and a polynomial-time method to verify network robustness for Byzantine fault tolerance.

Findings

The algorithm is provably correct under certain network conditions.

Strong-robustness can be efficiently checked in polynomial time.

Fundamental limitations are characterized based on network structure.

Abstract

Consider a linear time-invariant (LTI) dynamical system monitored by a network of sensors, modeled as nodes of an underlying directed communication graph. We study the problem of collaboratively estimating the state of the system when certain nodes are compromised by adversaries. Specifically, we consider a Byzantine adversary model, where a compromised node possesses complete knowledge of the system dynamics and the network, and can deviate arbitrarily from the rules of any prescribed algorithm. We first characterize certain fundamental limitations of any distributed state estimation algorithm in terms of the measurement and communication structure of the nodes. We then develop an attack-resilient, provably correct state estimation algorithm that admits a fully distributed implementation. To characterize feasible network topologies that guarantee success of our proposed technique, we introduce a notion of `strong-robustness' that captures both measurement and communication redundancy. Finally, by drawing connections to bootstrap percolation theory, we argue that given an LTI system and an associated sensor network, the `strong-robustness' property can be checked in polynomial time.