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.