Globally stable direct adaptive backstepping NN control for uncertain nonlinear strict-feedback systems

This paper investigates the problem of global tracking control for a class of nonlinear systems in the strict-feedback form with unknown system functions. By using radial basis function neural networks (RBFNNs) to compensate for system uncertainties, a novel switching controller is developed by combining direct adaptive control approach and backstepping technique, which consists of a conventional adaptive neural controller dominating in the neural active region and an extra robust controller to pull back the transient outside the neural active region. The key features of the proposed algorithm are given as follows. First, a novel nth-order smoothly switching function is presented, and then an energy-efficient controller is obtained. Second, only a neural network (NN) is employed to compensate for all the unknown parts in each backstepping design procedure to reduce the number of adaptive parameters, so that a more simplified controller is proposed. Third, by exploiting a special property of the affine term, the developed strategy avoids the controller singularity problem completely without using projection algorithm. As a result of the above features, the developed control algorithm is convenient to implement in applications. Finally, the overall controller ensures that all the signals in the closed-loop system are globally uniformly ultimately bounded (GUUB) and the output of the system converges to a small neighborhood of the reference trajectory by properly choosing the design parameters. Three simulation examples are given to illustrate the effectiveness of the proposed control scheme.