Distributed Data-driven Unknown-input Observers
CoRR(2024)
摘要
Unknown inputs related to, e.g., sensor aging, modeling errors, or device
bias, represent a major concern in wireless sensor networks, as they degrade
the state estimation performance. To improve the performance, unknown-input
observers (UIOs) have been proposed. Most of the results available to design
UIOs are based on explicit system models, which can be difficult or impossible
to obtain in real-world applications. Data-driven techniques, on the other
hand, have become a viable alternative for the design and analysis of unknown
systems using only data. In this context, a novel data-driven distributed
unknown-input observer (D-DUIO) for an unknown linear system is developed,
which leverages solely some data collected offline, without any prior knowledge
of the system matrices. In the paper, first, the design of a DUIO is
investigated by resorting to a traditional model-based approach. By resorting
to a Lyapunov equation, it is proved that under some conditions, the state
estimates at all nodes of the DUIO achieve consensus and collectively converge
to the state of the system. Moving to a data-driven approach, it is shown that
the input/output/state trajectories of the system are compatible with the
equations of a D-DUIO, and this allows, under suitable assumptions, to express
the matrices of a possible DUIO in terms of the matrices of pre-collected data.
Then, necessary and sufficient conditions for the existence of the proposed
D-DUIO are given. Finally, the efficacy of the D-DUIO is illustrated by means
of numerical examples.
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