Distributed Unknown Input Observer Design: A Geometric Approach
This work addresses the challenge of distributed state estimation in systems with unknown inputs, such as power grids, but it is incremental as it builds on existing geometric methods with relaxed conditions.
The paper tackles the problem of designing distributed unknown input observers for linear time-invariant systems with measurements spread across nodes, each affected by unknown inputs, by proposing a geometric approach that relaxes stringent rank conditions. The result is a method that enables state reconstruction under more relaxed conditions, validated through simulations including a power grid case study.
We present a geometric approach to designing distributed unknown input observers (DUIOs) for linear time-invariant systems, where measurements are distributed across nodes and each node is influenced by \emph{unknown inputs} through distinct channels. The proposed distributed estimation scheme consists of a network of observers, each tasked with reconstructing the entire system state despite having access only to local input-output signals that are individually insufficient for full state observation. Unlike existing methods that impose stringent rank conditions on the input and output matrices at each node, our approach leverages the $(C,A)$-invariant (conditioned invariant) subspace at each node from a geometric perspective. This enables the design of DUIOs in both continuous- and discrete-time settings under relaxed conditions, for which we establish sufficiency and necessity. The effectiveness of our methodology is demonstrated through extensive simulations, including a practical case study on a power grid system.