Remarks on folding behavior and plant Jacobian of neural network direct controller for its stability

Abstract

Simulation results of our previous papers show a neural network direct controller which performs well by the use of folding behavior. This paper presents an analytical approach for the questions related to the folding behavior. The intermediate value theorem answers these questions. There is the suitable plant input for any plant output, although the plant is nonlinear. The same sign of the plant Jacobian can be selected for any plant output. We can use the same sign of the neural network parameter η, although the plant is nonlinear. This paper also presents how we tune the neural network parameter η based on the above analytical approach. The approach of this paper deals with the static continuous nonlinear plant. However, I believe that it is helpful to understand the neural network performance for the dynamical plant. This paper also presents future works based on this analytical approach.