By Johann Schumann, Pramod Gupta, Yan Liu (auth.), Johann Schumann, Yan Liu (eds.)
"Applications of Neural Networks in excessive coverage platforms" is the 1st e-book at once addressing a key a part of neural community know-how: tools used to move the harsh verification and validation (V&V) criteria required in lots of safety-critical purposes. The ebook offers what different types of assessment equipment were constructed throughout many sectors, and the way to go the exams. a brand new adaptive constitution of V&V is constructed during this e-book, assorted from the easy six sigma tools frequently used for large-scale platforms and various from the theorem-based procedure used for simplified part subsystems.
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It should also be noted that Assumption 2 shows that a smaller μ implies that the approximation error of the residual nonlinearity using the approximator of local support functions needs to be smaller. This in turn can be accomplished by increasing N, the number of the support functions for a given μ and μc . For a given nonlinearity with a ﬁxed number of local support functions, namely N , the approximation error is ﬁxed which in turn determines μ in (44). This implies that in such a case, there is a certain compact domain M of e(t0 ) for which boundedness holds; no guaranties of boundedness can be given if e(t0 ) lies outside M.
2 Problem Statement The motivation for adaptive control stems from several causes including aerodynamic uncertainties, modeling inaccuracies, environmental disturbances and the fact that often actuators used in ﬂight control can exhibit various anomalies such as loss of eﬀectiveness, saturation, or failure, the last of which is our focus in this paper. The nonlinear ﬂight model in the presence of such actuator anomalies can be expressed as: X˙ = F (X, λU ) (1) where X ∈ n is the state vector that can be measured, and U is a scalar input.
An approach to determine the appropriate size of NN using Bayesian model comparison can be found in (40), where the neural networks with diﬀerent hidden neurons or hidden layers are considered as a set of diﬀerent models to be evaluated. It is based on the principle that the Bayesian formalism automatically penalizes the models with more complicated structures. A best model is the one which can balance the need of a large likelihood (so that it can ﬁt well with data) and the need of a network with simpler structure.