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| One considers ensembles (parameterized families) of nonlinear control systems
\mbox{$\dot{x}=f^\theta (x,u)$} with a parameter $\theta \in \Theta$ - finite-dimensional manifold.
One is interested in controlling all the systems of the ensemble by means of a single $\theta$-independent control $u(t)$.
It is known, that achieving exact controllability in such setting would require, in general, infinite-dimensional controls.
On the contrast we aim at criteria of {\it approximate ensemble controllability} by means of controls, which take their values in a space of fixed finite dimension.
We approach this infinite-dimensional problem setting by the tools of {\it geometric/Lie algebraic control} theory. We manage to provide sufficient approximate controllability criteria for ensembles of distributions as well as for Bloch system. The criteria are formulated in terms of Lie span condition, analogous to Lie rank controllability/acessibilty conditions, known in finite-dimensional case. |
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