Robust and Adaptive Backstepping Control for Nonlinear Systems Using RBF Neural Networks

TLDR

The paper proposes two backstepping neural network control approaches for affine nonlinear systems with unknown nonlinearities. Both approaches employ a special design scheme that eliminates controller singularities and permits performance shaping via design parameters. Simulations demonstrate that the closed‑loop signals are semiglobally uniformly ultimately bounded, the outputs converge to a small neighborhood of the desired trajectory, and the input differences between the two controllers are analyzed.

Abstract

In this paper, two different backstepping neural network (NN) control approaches are presented for a class of affine nonlinear systems in the strict-feedback form with unknown nonlinearities. By a special design scheme, the controller singularity problem is avoided perfectly in both approaches. Furthermore, the closed loop signals are guaranteed to be semiglobally uniformly ultimately bounded and the outputs of the system are proved to converge to a small neighborhood of the desired trajectory. The control performances of the closed-loop systems can be shaped as desired by suitably choosing the design parameters. Simulation results obtained demonstrate the effectiveness of the approaches proposed. The differences observed between the inputs of the two controllers are analyzed briefly.