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

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.