Neuro-adaptive command-filtered backstepping control of uncertain flexible-joint manipulators with input saturation via output

This paper addresses the challenging problem of precise trajectory tracking control for flexible-joint manipulators (FJMs) operating under intricate uncertainties, input-saturation constraints, and limited state feedback. Existing control strategies failed to simultaneously resolve the issues of input saturation and system uncertainties while relying solely on output feedback. Motivated by this limitation, we aim to propose a novel neuro-adaptive command-filtered output-feedback backstepping control scheme, which, to the best of our knowledge, is the first to integrate these capabilities for FJMs. The key findings include: (1) a smooth hyperbolic function combined with the mean-value theorem to effectively mitigate input-saturation effects; (2) an adaptive radial basis function (RBF) neural network-based state observer to estimate unmeasurable system states; and (3) a second-order command-filtered backstepping framework enhanced with error compensation dynamics to eliminate complexity explosion and reduce filtering errors. In addition, the proposed method eliminates the need for precise FJM models while ensuring uniform ultimate boundedness of all closed-loop signals, as rigorously proven via Lyapunov stability analysis. Comparative simulations demonstrate that the controller achieves superior transient and steady-state tracking accuracy over existing backstepping approaches.