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Furthermore, five ANFIS models with 6, 9, 19, 21 and 51 rules were developed utilizing the first order Sugeno fuzzy approach by back-propagation neural networks training algorithm.

Owing to utilizing the fourth-order cumulants and reweighted sparse representation framework, compared with ESPRIT-Like, FOC-MUSIC and l1-SVD algorithms, the proposed method performs well in both white and colored Gaussian noise conditions, meanwhile it has higher angular resolution and better angle estimation performance.

Utilizing the first-order condition of the above profit, the optimal order quantity is determined.

For the estimated value (hat{nu }_{text{s}}), the term ({mathcal{G}}left( t right)) demands the information of (mathop {mu_{text{a}} }limits^) and (dot{nu }_{text{s}}), which can be retrieved by utilizing the second-order sliding mode observer.

By utilizing the second-order sparse expression (13) and the single-channel sampling model (9), the single-channel sampling vector can be rewritten as begin{array}rcl@ {textbf{Y}_{1 M}} = {boldsymbol{bar Phi bar Psi chi }} + {boldsymbol{sigma }} end{array} (14).

The primary objectives of this paper are as follows: (A) We introduce a new set of formulas to be calculated at the tangent and cotangent factor nodes, to better approximate the mean and variance of the function values by utilizing the first-order TS expansion of the functions, so that the Gaussianity assumption still holds.

To utilize the first order grating, the diffraction efficiency is required on a very high level.

One approach is model-based and was presented by Yablonskiy et al., while the other approach utilizes the second order decay contribution that is predicted from the cumulant expansion theorem.

In [14], the author first presents the variational discretization concept for optimal control problems with control constraints, which implicitly utilizes the first order optimality conditions and the discretization of the state and adjoint equations for the discretization of the control instead of discretizing the space of admissible controls.

One utilizes the first-order and second-order reliability methods together with a hazard combination technique.

A possible solution is to utilize the first-order Taylor expansion technique associated with the preliminary CFO estimate in (21).