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Finite‐Time Optimal Tracking Control for Dynamic Systems on Lie Groups
Author(s) -
Liu Yongfang,
Geng Zhiyong
Publication year - 2015
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.946
Subject(s) - optimal control , backstepping , lie group , control theory (sociology) , euclidean group , tracking (education) , kinematics , mathematics , trajectory , euclidean geometry , computer science , maximum principle , mathematical optimization , control (management) , adaptive control , artificial intelligence , pure mathematics , psychology , pedagogy , physics , geometry , classical mechanics , astronomy , affine space , affine transformation
This paper investigates the problem of finite‐time optimal tracking control for dynamic systems on Lie groups for the situation when the tracking time and/or the cost functions need to be considered. The specific results are illustrated on SE(3) (the specific Euclidean groups of rigid body motions). The tracking time is given according to task requirements in advance. By using Pontryagin's maximum principle (PMP) on Lie groups and the backstepping method, a finite‐time optimal tracking control law is designed to track a desired reference trajectory at the given time. Simultaneously, the corresponding cost functions are guaranteed to be optimal. Compared with existing results of optimal control on Lie groups, it is noteworthy that we consider the finite‐time tracking control for dynamic systems rather than kinematic systems. Furthermore, the obtained optimal control law is described by explicit formulations, which is significant for practical applications.