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A specified‐time control framework for control‐affine systems and rigid bodies: A time‐rescaling approach
Author(s) -
Peng Xiuhui,
Sun Junyong,
Geng Zhiyong
Publication year - 2019
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4542
Subject(s) - affine transformation , control theory (sociology) , convergence (economics) , computer science , control (management) , synchronization (alternating current) , transformation (genetics) , control system , rotation (mathematics) , mathematics , engineering , artificial intelligence , computer network , channel (broadcasting) , biochemistry , chemistry , pure mathematics , electrical engineering , economics , gene , economic growth
Summary This paper addresses the specified‐time control problem for control‐affine systems and rigid bodies, wherein the specified‐time duration can be designed in advance according to the task requirements. By using the time‐rescaling approach, a novel framework to solve the specified‐time control problem is proposed, and the original systems are converted to the transformation systems based on which the specified‐time control laws for both control‐affine systems and rigid bodies are studied. Compared with the existing approaches, our proposed specified‐time control laws can be derived from the known stabilization control laws. To our best knowledge, it is the first time that transformation system–based specified‐time control framework for control‐affine system and rigid body dynamics is proposed. To further improve the convergence performance of specified‐time control, a finite‐time attitude synchronization control law for rigid bodies on rotation matrices is proposed, and thereby, the finite‐time–based specified‐time control law is designed eventually. In the end, numerical simulations and SimMechanics experiments are provided to illustrate effectiveness of the theoretical results.