Neural net backlash compensation with Hebbian tuning by dynamic inversion

A neural network compensation scheme is presented for the class of nonlinear systems with backlash nonlinearity. The compensator uses the backstepping technique with neural networks (NN) for inverting the backlash nonlinearity in the feedforward path. Instead of a derivative, which cannot be implemented, a filtered derivative is used. Full rigorous stability proofs are given using filtered derivative. Compared with adaptive backstepping control schemes, we do not require the unknown parameters to be linear parametrizable. No regression matrices are needed. The technique provides a general procedure for using NN to determine the dynamic preinverse of an invertible dynamical system. A modified Hebbian algorithm is presented for NN tuning which yields a stable closed-loop system. Using this method yields a relatively simple adaptation structure and offers computational advantages over gradient descent based algorithms