Discussion of neural network controllers from the point of view of inverse dynamics and folding behavior

Most of neural network controllers are designed so as to learn the inverse dynamics of the control object plant. However, the plant of the practical application usually has nonlinear characteristics and it is expressed as many to one function (whose one output corresponds to many input) mathematically. It is well known that there is no inverse function of the many to one function mathematically. What dose the neural network of above controllers learn? This paper discusses several neural network controllers from this point of view and their problem for realization of the neural network learning. On the other hand, it was confirmed that the neural network has the folding behavior in the neural network direct controller. This behavior is that the neural network learns only one part of the inverse of the object plant in order to obtain whole plant output. This means that we can realize the learning of the neural network direct controller without the direct inverse modeling. The complex structure of other neural network controllers is not necessary with regard to realize the neural network learning. This paper describes the details of above discussion and shows the simulation results of the neural network direct controller without the direct inverse modeling.