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The controller design approach guarantees the closed-loop stability and cost for all scheduled parameter changes.
Our paper deals with robust gain-scheduled controller design for uncertain LPV systems which ensures closed-loop stability and guaranteed cost for all scheduled parameter changes.
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A clustering technique based on an interpretation of belief functions combined to the least squares algorithm is used to estimate the scheduled parameters.
In the paper a new robust guaranteed cost output-feedback gain-scheduled PID controller design technique is presented for affine linear parameter-varying systems under polytopic model uncertainty, with the assumption that the scheduled parameters are affected with absolute uncertainty.
Its mathematical background relies on decision-functions determined by parameters and variables, being denoted by quantities chosen before any flight has been scheduled (parameters) and quantities depending on each flight (variables).
Experimental results show good tracking performance in the presence of scheduling parameter variations.
The GSOF controllers depend solely on scheduling parameters.
In contrast to the conventional problem setting, scheduling parameters are supposed to be provided with bounded absolute/proportional uncertainties.
Our approach is based on considering that the LPV system, scheduling parameters and their derivatives with respect to time lie in a priori given hyper rectangles.
The proposed controller is categorized as gain-scheduled controller because the PID gains are tuned using state variables as scheduling parameter.
The GS flight controller, which is scheduled by an inexactly provided scheduling parameter, viz.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com