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The normalisation is required because the unperturbed cost-of-fit and the maximum perturbed cost-of-fit are different for each parameter set.
The key technical step is to perturb the given comparison trajectory (tilde{textbf{v}}) in such a way that the perturbed trajectory has a cost that is close to (J tilde{u})), whereas it meets the manifolds where ({mathcal{V}}) is not differentiable only in a finite set of times.
Now, we will focus on the difference of states and cost functionals for the perturbed control and optimal control of minor agents.
In this paper we first generalize the notion of guaranteed cost controller to uncertain singularly perturbed systems, and then present a design procedure for a particular structure of uncertainties.
Both changes indicate that some of the observed large sensitivity in the uncoupled case was indeed due to high cost functions induced by mis-alignment of the slow dynamics of the perturbed and unperturbed models.
In [28], a primal-dual perturbed sub-gradient method is applied locally while averaging consensus is applied to estimate the global cost functions and constaints.
Because the implementation cost is reduced but the design complexity is increased, the determination of optimal positions of perturbed merging points requires a computationally efficient algorithm.
The advantages of the Asymptotic Perturbed-based Extremum Seeking Control scheme in comparison with other Extremum Seeking Control proposals are evaluated as (1) cost and complexity of implementation, and (2) performance obtained based on four indicators: the searching resolution, tracking accuracy, tracking efficiency, and tracking speed.
I remain a little perturbed.
Others are just plain perturbed.
You may be confused, or perturbed.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com