Nonlinear H-2 and H-infinity control formulated in the Weighted Sobolev space for underactuated mechanical systems with input coupling

Author(s)

Cardoso, Daniel N. ; Esteban, Sergio ; Raffo, Guilherme V. ; IEEE

• Document type: Journal article
• Source: 2018 IEEE CONFERENCE ON DECISION AND CONTROL (CDC); v. N/A, p. 6-pg., 2018-01-01.

Abstract

Two important paradigms in control theory are the nonlinear H-2 and H-infinity control approaches. Despite many advantages, such approaches present limitations in the sense to control the transient closed-loop response. An interesting approach to address these issues is the formulation of both controllers in the Sobolev space W-m,W-p. However, the latter also presents drawbacks, now in sense of weighting the cost variable and its time derivatives component-wise. Therefore, aiming to deal with underactuated mechanical systems with input coupling, this work presents a new formulation of the nonlinear H-2 and H-infinity control approaches in the Weighted Sobolev space W-m,W-p,W-sigma. It is also shown that for the particular systems treated in this work the W-2 and W-infinity optimal controllers are equivalent. In addition, a particular solution is proposed to the HJB and HJBI equations that arises from the problem formulation. The controller is corroborated by numerical experiments conducted with a quadrotor UAV. (AU)

• FAPESP's process: 14/50851-0 - INCT 2014: National Institute of Science and Technology for Cooperative Autonomous Systems Applied in Security and Environment
• Grantee: Marco Henrique Terra
• Support Opportunities: Research Projects - Thematic Grants