scholarly journals Motion control of drift-free, left-invariant systems on Lie groups

1995 ◽  
Vol 40 (9) ◽  
pp. 1539-1554 ◽  
Author(s):  
N.E. Leonard ◽  
P.S. Krishnaprasad
Keyword(s):  
Lie Groups ◽  
Motion Control ◽  
Free Left ◽  
Systems On Lie Groups

State estimation for invariant systems on Lie groups with delayed output measurements

Automatica ◽  
2016 ◽  
Vol 68 ◽  
pp. 254-265 ◽  
Author(s):  
Alireza Khosravian ◽  
Jochen Trumpf ◽  
Robert Mahony ◽  
Tarek Hamel
Keyword(s):  
State Estimation ◽  
Lie Groups ◽  
Systems On Lie Groups

Cost-Extended Control Systems on Lie Groups

2013 ◽  
Vol 11 (1) ◽  
pp. 193-215 ◽  
Author(s):  
R. Biggs ◽  
C. C. Remsing
Keyword(s):  
Control Systems ◽  
Lie Groups ◽  
Systems On Lie Groups

scholarly journals Attainable sets and one-parameter semigroups of sets

1991 ◽  
Vol 33 (2) ◽  
pp. 187-201 ◽  
Author(s):  
I. Chon ◽  
J. D. Lawson
Keyword(s):  
Control Systems ◽  
Lie Groups ◽  
Vector Fields ◽  
Geometric Control ◽  
Lie Theory ◽  
Attainable Sets ◽  
Widespread Application ◽  
Close Relationship ◽  
Basic Facts ◽  
Systems On Lie Groups

The methods of Lie theory have found widespread application in the study of the Lie algebras of vector fields on manifolds that arise naturally in geometric control theory (for some such applications, see [1]). Control systems on Lie groups themselves also have received considerable attention (see, for example, [9]). After reviewing basic facts about control systems on Lie groups, we derive the close relationship between attainable sets and Rådström's theory [12] of one-parameter semigroups of sets (Section 2). These ideas are then linked to the recently emerging Lie theory of semigroups [5]. The authors are indebted to the referee for pointing out some of the pertinent literature and analogous results from the area of geometric control.

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