Neural network control for a closed-loop System using Feedback-error-learning

This paper presents new learning schemes using feedback-error-learning for a neural network model applied to adaptive nonlinear feedback control. Feedback-error-learning was proposed as a learning method for forming a feedforward controller that uses the output of a feedback controller as the error for training a neural network model. Using new schemes for nonlinear feedback control, the actual responses after learning correspond to the desired responses which are defined by an inverse reference model implemented as a conventional feedback controller. In this respect, these methods are similar to Model Reference Adaptive Control (MRAC) applied to linear or linearized systems. It is shown that learning impedance control is derived when one proposed scheme is used in Cartesian space. We show the results of applying these learning schemes to an inverted pendulum and a 2-link manipulator. We also discuss the convergence properties of the neural network models employed in these learning schemes by applying the Lyapunov method to the averaged equations associated with the stochastic differential equations which describe the system dynamics. Keywords-Neural network control, Adaptive control, Feedback-control learning, Reference model, Impedance control, Feedback-error-learning, Cerebellum motor control learning.