A New Method for the Analysis of Neural Reference

In recent years there has been much eeort to develop the theoretical aspects of neural MRAC-Control, that is to nd conditions under which an unknwon process can be identiied by an input-output model and controllers can be trained by gradient descent ((3],,6]). On the other hand, the application of neural network techniques to real world control of nonlinear dynamical systems has been of substantial interest. Since the theoretical conditions that ensure controllability and the applicability of indirect adaptive control are hard to verify in practice, the success of controller training is mostly shown by testing relevant situations. We trained a controller for a subsystem of a spark ignition engine by dynamic backpropagation ((2]) and various truncated gradient algorithms. After-wards we related the neural MRAC-approach to Pole placement and Linearization techniques in order to show the successful training by Pole analysis of the completely trained loop. This is a new method to verify the plausibility of the adaptation process and the trained regulator.