arXiv:2611.08762v1 Announce Type: new Abstract: In this paper, a computationally efficient robust adaptive Lyapunov-based model predictive control (RALMPC) framework is proposed for a class of constrained nonlinear systems subject to uncertainties and external disturbances. A radial basis function neural network (RBFNN), introduced to approximate non-parametric uncertainties, is incorporated into a control Lyapunov function analysis, together with integral barrier Lyapunov functionals for state constraint enforcement. This analysis yields control and adaptation laws for parametric uncertainties, external disturbances, RBFNN weights, and worst-case approximation error, rendering the closed-loop system uniformly bounded while ensuring convergence of tracking errors to compact sets around the origin. The resulting guarantees are then embedded into the RALMPC optimal control problem through a contractive constraint, thus combining formal closed-loop stability with real-time performance optimization; at the same time, the adaptation laws allow the RALMPC prediction model to be updated online. Comparative hardware-in-the-loop simulations against state-of-the-art MPC schemes validate the efficacy and computational efficiency of the proposed framework. Ultimately, RALMPC is experimentally validated on a custom-built quadcopter platform for time-varying attitude tracking, demonstrating its practical feasibility; comparisons against alternative strategies confirm its superiority in achieving improved closed-loop performance.