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Lyapunov theory is used to guarantee stability for state estimation and neural network weight errors.
Lyapunov techniques are used to demonstrate the convergence of the NN weight errors in the sense of uniform ultimate bounded.
The network weight adaptation rule is derived from Lyapunov stability analysis, and guarantees that the adapted weight errors and the tracking error are bounded.
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The weight error is defined to be (11).
where the weight error vector is given by w ̃ ( n ) = w ( n ) - h (26).
was applied.3 In the literature, (tilde {{mathbf {w}}}_{k}) is also often referred to as weight error vector, w k as weight estimate, and K k as weight error vector covariance matrix.
A multilayer feed-forward ANN model, with Levenberg Marquardt weight error correction was used for data modeling.
To find the mean weight error, we need to take the expectation of Eq. (45), and relying on the assumptions A1 A4, the noise is independent of the input signal as well as the weight error vector.
A.2 The weight error vector (v n ), to be defined later, is independent of the input x n.
Both the mean and the mean-square behaviors of the weight error vector are presented in the ensuing analysis.
The weight error vector is defined as boldsymbol{v}(n)=boldsymbol{w}(n -{boldsymbol{w}}_{boldsymbol{o}}.
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