We formulate a novel learning algorithm for output zeroing of linear f
inite-dimensional, control systems. As in classical control systems th
eory, we start from the knowledge of a nominal plant to develop a feed
back algorithm that achieves the control objective by means of success
ive trials on the plant. Algorithm convergence in the face of linear p
lant perturbations is proved, and performance in the face of small non
linear perturbations is discussed. The proposed algorithm does not req
uire output differentiation, and is based upon the learning of the ini
tial conditions that allow the output to remain identically zero, whil
e the state of the system, dynamically extended, freely evolves comply
ing with an internal stability constraint. Implementation of this algo
rithm requires state initialization at an arbitrary point of the state
space. Therefore, for those systems for which direct state initializa
tion is not feasible, we develop a learning procedure that automatical
ly accomplishes this task. By means of a control input generated by th
e algorithm, the state of the system is steered, during an initial pha
se, from a point where it is easily initialized to the point from whic
h the output zeroing task starts. An illustrative example is included.