Adaptive neural control for nonlinear systems in non-strict-feedback form

This article studies the ANC problem for nonlinear systems. Unlike the classical backstepping strategy, the control issue of nonlinear system in non-strict feedback(NSF) form is more challenging. In the design process, neural networks and high-gain observers are applied to tackle with the issues of unknown nonlinearity and unmeasured states, respectively. Adaptive backstepping technique and a high-order sliding mode (HOSM) differentiator are combined to present a novel ANC algorithm. In the stability analysis, signals in the considered systems turn to be SGGB with appropriately designed parameters. Finally, a numerical example is practiced. The results of the numerical simulation further illustrate the usefulness of the new algorithm.