n-Dimensional controllability with(n-1)controls
- 1 February 1982
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 27 (1) , 113-117
- https://doi.org/10.1109/tac.1982.1102876
Abstract
Let M be a connected real-analytic n -dimensional manifold, f, g_{1}, ... ,g_{n-1} be complete real-analytic vector fields on M which are linearly independent at some point of M , and u_{1}, ... , u_{n-1} be real-valued controls. Consider the controllability of the system \dot{x}(t)=f(x(t)) + \sum\min{i=1}\max{n-1} u_{i}(t)g_{i}(x(t)), x(0)=x_{0} \in M . Necessary and sufficient conditions are given so that this system is controllable on any simply connected domain D contained in M on which g_{1},... ,g_{n-1} are linearly independent. These conditions depend on the computation of Lie brackets at those points where f, g_{1}, ... ,g_{n-1} are linearly dependent.Keywords
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