  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.
