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We study possibilities to control an ensemble (a parameterized family) ofnonlinear control systems by a single parameter-independent control. Proceedingby Lie algebraic methods we establish genericity of exact controllabilityproperty for finite ensembles, prove sufficient approximate controllabilitycondition for a model problem in $\mathbb{R}^3$, and provide a variant ofRashevsky-Chow theorem for approximate controllability of control-linearensembles.

Ensemble controllability by Lie algebraic methods