Giorgia Disarò

This article addresses the distributed state estimation problem for a discrete-time linear and time-invariant (LTI) state-space model, whose state equation is affected by disturbances. A connected sensor network, in which each sensor has access only to part of the control inputs and provides its own output signal (that represents a partial indirect measurement of the state), is deployed to reconstruct the state of a system. Such sensors exchange information with the goal of achieving consensus and providing an asymptotically correct estimate of the global system state. Necessary and sufficient conditions for the existence of distributed unknown input observers (DUIOs) with augmented states that achieve both goals are derived. Moreover, an algorithmic procedure to design the matrices of the proposed DUIO is presented. The problem solution leverages the theory of decentralized output feedback control, thus making it possible to exploit the algorithms available for the solution of that problem.

In this paper we investigate a data-driven approach to the design of an unknown-input observer (UIO). Specifically, we provide necessary and sufficient conditions for the existence of an unknown-input observer for a discrete-time linear time-invariant (LTI) system, designed based only on some available data, obtained on a finite time window. We also prove that, under weak assumptions on the collected data, the solvability conditions derived by means of the data-driven approach are in fact equivalent to those obtained through the model-based one. In other words, the data-driven conditions do not impose further constraints with respect to the classic model-based ones, expressed in terms of the original system matrices.