Controllability of some nonlinear systems with drift via generalized curvature properties
SIAM Journal on Control and Optimization, ISSN: 0363-0129, Vol: 53, Issue: 1, Page: 434-474
2015
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Article Description
We discuss the problem of local attainability for finite-dimensional nonlinear control systems with quite general assumptions on the target set. Special emphasis is given to control-affine systems with a possibly nontrivial drift term. To this end, we provide some sufficient conditions ensuring local attainability, which involve geometric properties both of the target itself (such as a notion of generalized curvature), and of the Lie algebra associated with the control system. The main technique used is a convenient representation formula for the power expansion of the distance function along the trajectories, made at points sufficiently near to the target set.
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