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.

Invertibility of Control Systems on Lie Groups

1977 ◽  
Vol 15 (6) ◽  
pp. 1034-1049 ◽  
Author(s):  
Ronald M. Hirschorn
Keyword(s):  
Control Systems ◽  
Lie Groups ◽  
Systems On Lie Groups

scholarly journals Control systems on Lie groups

1972 ◽  
Vol 12 (2) ◽  
pp. 313-329 ◽  
Author(s):  
Velimir Jurdjevic ◽  
Héctor J Sussmann
Keyword(s):  
Control Systems ◽  
Lie Groups ◽  
Systems On Lie Groups

Solutions of singular control systems on lie groups

2012 ◽  
Vol 18 (3) ◽  
pp. 323-338
Author(s):  
V. Ayala ◽  
J. C. Rodríguez ◽  
I. A. Tribuzy ◽  
C. Wagner
Keyword(s):  
Control Systems ◽  
Lie Groups ◽  
Singular Control ◽  
Systems On Lie Groups

scholarly journals Outer invariance entropy for discrete-time linear systems on Lie groups

2021 ◽  
Author(s):  
Fritz Colonius ◽  
João A.N. Cossich ◽  
Alexandre J. Santana
Keyword(s):  
Control Systems ◽  
Lie Groups ◽  
Discrete Time ◽  
Upper Bound ◽  
Linear Control Systems ◽  
Invariance Entropy ◽  
Admissible Pairs ◽  
Systems On Lie Groups ◽  
Time Linear ◽  
Uncontrolled System

We introduce discrete-time linear control systems on connected Lie groups and present an upper bound for the outer invariance entropy of admissible pairs (K,Q). If the stable subgroup of the uncontrolled system is closed and K has positive measure for a left invariant Haar measure, the upper bound coincides with the outer invariance entropy.

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