# Byzantine-Resilient Distributed Observers for LTI Systems

arXiv: https://arxiv.org/abs/1802.09651 · HTML: https://mlsanity.com/paper/1802.09651/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2018.

## Built on by (most cited first, 3 of 3)

- [Exploiting Heterogeneity in Robust Federated Best-Arm Identification](https://mlsanity.com/paper/2109.05700/) (2021)
- [Design and Analysis of Robust Resilient Diffusion over Multi-Task Networks Against Byzantine Attacks](https://mlsanity.com/paper/2206.12749/) (2022)
- [Resilient Output Consensus Control of Heterogeneous Multi-agent Systems against Byzantine Attacks: A Twin Layer Approach](https://mlsanity.com/paper/2303.15299/) (2023)

## Abstract (arXiv)

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.