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This paper presents an adaptive back-stepping neural controller for reconfigurable flight control of aircraft in the presence of large changes in the aerodynamic characteristics and also failures. In the proposed controller, radial basis function (RBF) neural networks are utilized in an adaptive back-stepping architecture with full state measurement. For the RBF neural networks, a learning scheme in which the network starts with no hidden neurons and adds new hidden neurons based on the trajectory error is developed. Using the Lyapunov theory, stable tuning rules are derived for the update of the centers, widths, and weights of the RBF neural networks and a proof of stability in the ultimate bounded sense is given for the resulting controller. The theory is illustrated using the longitudinal model of an open-loop unstable high-performance aircraft in the terminal landing phase subjected to single elevator hard over failure and severe winds. The resulting controller is able to successfully stabilize and land the aircraft within a tight touch down dispersion.