Data-Driven Unknown Input Reconstruction for MIMO Systems with Convergence Guarantees

TL;DR

This paper introduces a data-driven method for reconstructing unknown inputs in MIMO systems using a novel autoregressive estimator with convergence guarantees, relying solely on recorded data.

Contribution

It presents a new input reconstruction estimator that does not require system knowledge and guarantees stability based on data-derived invariant zeros.

Findings

Estimator is strictly stable if invariant zeros are inside the unit circle.

Method relies on Hankel matrix-based least squares without true input knowledge.

Numerical examples validate theoretical stability and reconstruction accuracy.

Abstract

In this paper, we consider data-driven reconstruction of unknown inputs to linear time-invariant (LTI) multiple-input multiple-output (MIMO) systems. We propose a novel autoregressive estimator based on a constrained least-squares formulation over Hankel matrices, splitting the problem into an output-consistency constraint and an input-history-matching objective. Our method relies on previously recorded input-output data to represent the system, but does not require knowledge of the true input to initialize the algorithm. We show that the proposed estimator is strictly stable if and only if all the invariant zeros of the trajectory-generating system lie strictly inside the unit circle, which can be verified purely from input and output data. This mirrors existing results from model-based input reconstruction and closes the gap between model-based and data-driven settings. Lastly, we provide numerical examples to demonstrate the theoretical results.