Nonlinear H2 and H∞ control formulated in the Sobolev space for mechanical systems
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Universidade Federal de Minas Gerais
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Nonlinear H2 and H-infinity control formulated in the Sobolev space for mechanical systems
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Two important paradigms in control theory are the classic nonlinear H2 and H∞ control approaches. Their background theory are well developed, and several applications have demonstrated their efficiency. Despite many advantages, they suffer from deficiencies such as minimum settling-time and minimum overshoot. An interesting approach to solve these limitations is the formulation of both controllers in the Sobolev space. Thanks to the nature of the W - norm, the cost variable and its time derivatives are taken into account in the cost functional, leading to controllers with improved transient and steady-state performance. Thus, aiming to deal with mechanical systems this work reformulates the H2 and H∞ controllers in the Sobolev space. It is shown that, for particular systems, the W2 and W∞ optimal controllers are equivalent. An optimal solution for the class of fully actuated mechanical systems is proposed. The controller is corroborated by numerical experiments conducted with a quadrotor UAV.
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Aeronave não tripulada, Sistemas não lineares
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Nonlinear systems, H2 control, H-infinity control, Sobolev space, Robust control, mechanical systems, nonlinear H-infinity control design in robotic systems under parameter perturbation and external disturbance
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https://www.sciencedirect.com/science/article/pii/S2405896318327496