Abstract
This chapter deals with a bounded control design for a class of nonlinear systems whose mathematical model may not be explicitly given. This class of uncertain nonlinear systems is governed by a system of ordinary differential equations with quasi-Lipschitz right-hand sides and contains external perturbations as well. The attractive ellipsoid method (AEM) allows us to describe the class of nonlinear feedbacks (containing a nonlinear projection operator, a linear state estimator, and a feedback matrix gain) guaranteeing the boundedness of all possible trajectories around the origin. To satisfy this property, some modifications of the AEM are introduced: basically, some sort of sample-time corrections of the feedback parameters are required. The optimization of feedback within this class of controllers is associated with the selection of the feedback parameters such that the trajectory converges within an ellipsoid of “minimal size.” The effectiveness of the suggested approach is illustrated by its application to a flexible arm system.
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Poznyak, A., Polyakov, A., Azhmyakov, V. (2014). Bounded Robust Control. In: Attractive Ellipsoids in Robust Control. Systems & Control: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-09210-2_11
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DOI: https://doi.org/10.1007/978-3-319-09210-2_11
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