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Based on a guaranteed LPV approximation, the problem of set observers design is recasted into more general adaptive observers design problem in order to avoid the exponential complexity obstruction usually met in the set-membership nonlinear estimation.
Khan et al. [12] investigated, by employing the homotopy perturbation transform method (HPTM) and the Padé approximation, the problem of magnetohydrodynamic (MHD) boundary layer flow over a nonlinear porous stretching sheet.
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We show that, by making further simplifying approximations, the problem can be recast into a convex optimization problem.
The big approximation is your approximation to the problem you want to solve.
We now introduce the Galerkin approximation for the problem (1.1 - 1.2 1.1 - 1.2
The optimality conditions in (3.20 - 3.22) are the semi-discrete approximation to the problem (3.3 - 3.5 3.3 - 3.5
Let us consider the question about validity of applicability of the WKB approximation to the problem under consideration.
Finally, we show the obtained solutions are proper approximation for the problem under the Euclidean distance.
Using the approximation models, the problem is reduced to a linear system of equations, which has as unknowns the nodal values of the sources intensities.
In the following we shall employ, in fact, the solutions obtained in Ref. [26] as the zeroth approximation of the problem with a doped dot.
More generally, the model described here uses a simple linear response model and thus clearly only implements a rough approximation to the problem solved by the nervous system.
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