On controller design for systems on manifolds in Euclidean space

Summary A new method is developed to design controllers in Euclidean space for systems defined on manifolds. The idea is to embed the state‐space manifold M of a given control system into some Euclidean space Rn, extend the system from M to the ambient space Rn, and modify it outside M to add transv...

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Bibliographic Details
Published in:International journal of robust and nonlinear control 2018-11, Vol.28 (16), p.4981-4998
Main Author: Chang, Dong Eui
Format: Article
Language:English
Subjects:
Cartesian coordinates
Control stability
Control systems design
Controllers
Coordinates
Design engineering
drone
Dynamic stability
Embedded systems
embedding
Euclidean geometry
Euclidean space
manifold
Manifolds
quadcopter
rigid body
Rigid structures
Synthesis
tracking
Tracking problem
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Summary:Summary A new method is developed to design controllers in Euclidean space for systems defined on manifolds. The idea is to embed the state‐space manifold M of a given control system into some Euclidean space Rn, extend the system from M to the ambient space Rn, and modify it outside M to add transversal stability to M in the final dynamics in Rn. Controllers are designed for the final system in the ambient space Rn. Then, their restriction to M produces controllers for the original system on M. This method has the merit that only one single global Cartesian coordinate system in the ambient space Rn is used for controller synthesis, and any controller design method in Rn, such as the linearization method, can be globally applied for the controller synthesis. The proposed method is successfully applied to the tracking problem for the following two benchmark systems: the fully actuated rigid body system and the quadcopter drone system.
ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.4294