Rigorous fully distributed observability-blocking algorithms

Develop rigorous and provable algorithms for a fully distributed solution to the observability-blocking control problem in which actuation nodes rely on local observations and inter-actuation-node communication, including jointly designed distributed observers and controllers.

Background

The paper develops a distributed extension of its observer-based observability-blocking method. Each actuation node constructs an observer using its own state and neighboring-state measurements, while actuation nodes communicate their control signals or state estimates. When every local actuation-node observation pair is observable, the observer gains can be designed independently and the state-feedback controller can be constructed using an existing observability-blocking algorithm.

The paper also considers the more difficult case in which individual actuation-node observation pairs are not observable but are collectively observable. In that setting, the observers must exchange estimates and include consensus terms. Their gains must be designed jointly, either heuristically or through linear matrix inequality techniques, subject to a collective stability condition. The authors explicitly leave the development of rigorous, provable algorithms for this fully distributed setting unresolved.

References

We leave the development of rigorous and provable algorithms for a fully distributed solution to the observability blocking problem in future work.

— Observability Blocking in a Linear Synchronization Network with Partial State Measurements  (2608.25259 - Moreno et al., 26 Aug 2026) in Section III-C, "A Distributed Framework"

Yet, the problem remains open. The algorithms proposed in , Sec.~4, effectively operate over time-varying networks, but require a centralized design procedure and thus do not support plug-and-play operation. The algorithms considered in allow both decentralized design and operation over switching networks, but require the network to relay all previously communicated information , remain strongly connected despite switching , or switch sufficiently fast\footnote{As discussed in , fast switching may not be achievable in practice if the source of switching is unreliability of communication channels.} , thereby necessitating fairly reliable network conditions. The algorithms introduced in Sec.~3, allow decentralized design while being well-suited for operation over unreliable networks. However, they apply only to specific classes of systems: Sec.~3, require each pair $(A\top,C_i\top)$ to be marginally stabilizable, and require system eqn:system to be neutrally stable.

— On stability of a distributed observer over switching networks: The case of commutative coupling  (2609.26065 - Koo et al., 22 Sep 2026) in Section 1, Introduction