Geodesic
Ensemble controllability by Lie algebraic methods
Agrachev, Andrei1, 2  ; Baryshnikov, Yuliy3 ; Sarychev, Andrey4 
1 International School for Advanced Studies (SISSA), v. Bonomea, 265, 34136 Trieste, Italy
2 Steklov Mathematical Institute, Russian Acad. Sciences, Moscow, Russia
3 University of Illinois at Urbana-Champaign 1409 W. Green Str., Urbana IL 61801, USA
4 University of Florence, DiMaI, v. delle Pandette 9, 50127 Firenze, Italy
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 921-938

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We study possibilities to control an ensemble (a parameterized family) of nonlinear control systems by a single parameter-independent control. Proceeding by Lie algebraic methods we establish genericity of exact controllability property for finite ensembles, prove sufficient approximate controllability condition for a model problem in R 3 , and provide a variant of Rashevsky−Chow theorem for approximate controllability of control-linear ensembles.

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DOI : 10.1051/cocv/2016029
Classification : 93C15, 93B05, 93B27
Keywords: Infinite-dimensional control systems, ensemble controllability, Lie algebraic methods

Agrachev, Andrei 1, 2 ; Baryshnikov, Yuliy 3 ; Sarychev, Andrey 4

1 International School for Advanced Studies (SISSA), v. Bonomea, 265, 34136 Trieste, Italy
2 Steklov Mathematical Institute, Russian Acad. Sciences, Moscow, Russia
3 University of Illinois at Urbana-Champaign 1409 W. Green Str., Urbana IL 61801, USA
4 University of Florence, DiMaI, v. delle Pandette 9, 50127 Firenze, Italy 
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     title = {Ensemble controllability by {Lie} algebraic methods},
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     pages = {921--938},
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Agrachev, Andrei; Baryshnikov, Yuliy; Sarychev, Andrey. Ensemble controllability by Lie algebraic methods. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 921-938. doi: 10.1051/cocv/2016029

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