Adaptive Tracking of SISO Nonlinear Systems Using Multilayered Neural Networks

Multilayered neural networks (MNNs) are used in this paper to construct the nonlinear learning control systems for a class of unknown nonlinear systems in a canonical form. An adaptive output tracking architecture is proposed using the outputs of two three-layered neural networks which are trained to approximate an unknown nonlinear plant to any desired degree of accuracy by using the back-propagation method. The weight updating algorithm is presented using the gradient descent method with a dead-zone function. Convergence of the error index during the weight training is also shown. The closed system is proved to be stable, with output tracking error converging to a neighborhood of the origin. The effectiveness of the control scheme proposed is illustrated through simulations.