Robustness of a neural controller in the presence of additive and multiplicative external perturbations

In this paper we discuss the tracking problem in the presence of additive and multiplicative external disturbances, for affine in the control nonlinear dynamical systems, whose nonlinearities are assumed unknown. Based on a recurrent high-order neural network (RHONN) model of the unknown plant, a smooth control law is designed to guarantee the uniform ultimate boundedness of all signals in the closed loop. Certain measures are utilized to test its performance. The controller, which can be viewed as a nonlinear combination of three high-order neural networks (HONN), does not require knowledge regarding upper bounds on the optimal weights, modeling error and external disturbances. Simulations performed on a simple example illustrate the approach.