Data-Driven Inverse of Linear Systems and Application to Disturbance Observers

TL;DR

This paper proposes a data-driven method to invert linear systems for reconstructing inputs from outputs, enabling disturbance observation without explicit plant models, based on data invertibility conditions and persistent excitation.

Contribution

It introduces a novel data-based inverse dynamics construction for LTI systems and applies it to develop a disturbance observer that operates without explicit plant models.

Findings

The inverse problem is solvable under L-delay invertibility and persistent excitation.

The data-driven disturbance observer achieves disturbance rejection without plant model knowledge.

The approach extends behavioral system theory to inverse and control applications.

Abstract

This work develops a data-based construction of inverse dynamics for LTI systems. Specifically, the problem addressed here is to find an input sequence from the corresponding output sequence based on pre-collected input and output data. The problem can be considered as a reverse of the recent use of behavioral approach, in which the output sequence is obtained for a given input sequence by solving an equation formed by pre-collected data. The condition under which the problem gives a solution is investigated and turns out to be L-delay invertibility of the plant and a certain degree of persistent excitation of the data input. The result is applied to form a data-driven disturbance observer. The plant dynamics augmented by the data-driven disturbance observer exhibits disturbance rejection without the model knowledge of the plant.