Ensemble controllability by Lie algebraic methods. (English) Zbl 1350.93014
Summary: 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 \(\mathbb{R}^3\), and provide a variant of Rashevsky-Chow theorem for approximate controllability of control-linear ensembles.
MSC:
| 93B05 | Controllability |
| 93B27 | Geometric methods |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93C10 | Nonlinear systems in control theory |
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