Neural Network-Based Adaptive Command Filtered Backstepping Design for Uncertain Second-Order Strict-Feedback Systems

A neural network-based adaptive command filtered backstepping control scheme is proposed for a class of second-order strict-feedback systems with smooth uncertain nonlinear functions. The proposed control scheme approximates the unknown smooth nonlinear function in the SFSs using RBF neural network. Unlike existing classical first-order state-space methods, command filters are introduced in the backstepping design, significantly reducing the complexity of designing control laws, overcoming the problem of “explosion of complexity”. Furthermore, the proposed scheme avoids converting a second-order system into a first-order system and allows for fewer and easier steps. Stability analysis of the closed-loop system shows that, by appropriately adjusting the design parameters, it is possible to ensure that all signals in the closed-loop system are uniformly ultimately bounded, and this bound can be arbitrarily small.