In this paper, the adaptive neural network based online limit and control margin estimation algorithms for envelope protection are improved using a non-iterative limit margin estimation methodology. The fixed point solution assumption is removed. Functional relations between the fast aircraft states and the control inputs are generated online using concurrent learning neural networks with guaranteed signal bounds. Estimates of the optimal adaptive weights are obtained through concurrent adaptation using minimum singular value maximization for recording necessary data. The allowable control travel not to exceed an imposed flight envelope limit is estimated using control sensitivity estimations. This information can be used to cue pilots or limit controller commands to ensure a safe flight. A nonlinear aircraft model is used to show the effectiveness in simulation.
NomenclatureA 1 , A 2 , B = matrices of linear system φ = neural network basis e = model tracking error vector φ = activation function f , f 1 , f 2 = vectors of nonlinear functions ξ = modeling error vector n z = load factor θ = pitch angle q = pitch rate δ e = elevator input S = sensitivity vector Γ = neural network learning gain tr(.) = trace operator ∆ = vector of neural networks u = control input vector∂(.) = central difference operator u e = single effective control input ∂(.) = average sum operator u = control vector without u e = reconstruction error vector V = Lyapunov function Subscripts V e = indicated airspeed DT = dynamic trim W = weight matrix f = fast x = system state vector s = slow x = neural network input vector lim = limit Z = history stack matrix marg = limit or control margin α = angle of attackˆ= approximation