Byzantine-Resilient Distributed Observers for LTI Systems
For control systems relying on distributed sensor networks, this work provides a rigorous framework and algorithm to ensure state estimation despite worst-case adversarial attacks.
The paper addresses distributed state estimation for LTI systems under Byzantine attacks, where compromised nodes can arbitrarily deviate. It characterizes fundamental limitations and proposes a provably correct algorithm with a polynomial-time checkable network property called strong-robustness.
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.