Nonlinear H2 and H∞ control formulated in the Sobolev space for mechanical systems⁎. Issue 25 (2018) - Cardoso, Daniel N.; Raffo, Guilherme V.; Esteban, Sergio
Abstract: Two important paradigms in control theory are the classic nonlinear H 2 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 H 2 and H ∞ controllers in the Sobolev space. It is shown that, for particular systems, the W 2 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.