Nonlinear H2 and H∞ control formulated in the Sobolev space for mechanical systems⁎. Issue 25 (2018)

• Record Type: Journal Article
• Authors: Cardoso, Daniel N.; Raffo, Guilherme V.; Esteban, Sergio
• Is Part Of: IFAC-PapersOnLine. Volume 51:Issue 25(2018)
• Page Start: 96
• Page End: 101
• Publication Date: 2018
• Subjects: Nonlinear systems -- H2 control -- H∞ control -- Sobolev space -- Robust control -- mechanical systems; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2018.11.088
• Languages: English
• ISSNs: 2405-8963

Abstract

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.