Valid RBFNN adaptive control for pure‐feedback nonlinear systems with unmatched uncertainties

Abstract This paper proposes an adaptive control approach utilizing radial basis function neural networks (RBFNNs) to manage pure‐feedback nonlinear systems with unmatched uncertainties. The validity issue of RBFNN‐based adaptive control was essentially tackled by ensuring that all associated closed‐loop signals are semi‐global uniformly ultimately bounded. The control strategy incorporates adaptive parameter gains, and it is shown that adjusting these gains can significantly enhance control performance. System modeling incorporates both ideal RBFNNs and their online estimation versions, where initial compact sets are strictly verified to fulfill the validity requirement within a finite time interval. The approach extends finite‐time validity to infinite time by reconstructing compact sets. Finally, the overall effectiveness and feasibility of the proposed control strategy are demonstrated through comprehensive simulation results.