  An increasing trend in the use of neural networks in control systems is being
observed. The aim of this paper is to reveal that the straightforward
application of learning neural network feedforward controllers with closed-loop
data may introduce parameter inconsistency that degrades control performance,
and to provide a solution. The proposed method employs instrumental variables
to ensure consistent parameter estimates. A nonlinear system example reveals
that the developed instrumental variable neural network (IVNN) approach
asymptotically recovers the optimal solution, while pre-existing approaches are
shown to lead to inconsistent estimates.
