Neuro-Adaptive Finite-Time Command-Filter Backstepping Control of Full State Feedback Nonlinear System

This work develops a neuro-adaptive finite-time command-filtered backstepping (CFB) control framework for full-state feedback systems. The design methodology initiates with error transformation techniques to embed finite-time prescribed performance (FT-PP) specifications into the control architecture. Building upon this foundation, a dynamic error compensation system is formulated to neutralize filtering artifacts induced by the finite-time command filter (FT-CF), thereby achieving precise finite-time convergence. To address state estimation requirements, we construct a neural network-based state estimation framework utilizing radial basis function neural networks (RBFNNs) for simultaneous uncertainty approximation and unmeasurable state reconstruction. The synthesis of FT-PP constraints and neural state estimation culminates in the derivation of an adaptive control law with Lyapunov-stable update rules, theoretically ensuring tracking errors enter and remaining within small neighborhoods of target compact sets within predefined finite time horizons. The simulation experiments cover both numerical simulation and actual case studies, which verify the feasibility and effectiveness of the proposed control mode.