In this paper, two vital signals to enable flight envelope protection, namely the onset to the flight envelope (limit margin) and the available control travel to reach the limit boundary (control margin), are estimated using improved noniterative adaptive neural-network-based approximate models. The adaptive elements use current and past information (concurrent learning) and have guaranteed signal bounds. Minimum singular value maximization is used to record data for concurrent learning. Results showed better convergence properties of the network weights compared with results in the literature in which only the current data is used for network weight updates. Two methods are introduced to calculate control margins from approximate models. None of the introduced methods require iteration and therefore remove previously introduced assumptions related to iteration convergence. A nonlinear fixed-wing aircraft model is used to show the effectiveness in simulation for estimating limit and control margins and avoiding the limit through artificial control saturation.