ISSN:
1433-0490
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
Notes:
Abstract LetM be a connected real-analytic 2-dimensional manifold. Consider the system $$\dot x(t) = f(x(t)) + u(t)g(x(t)),x(0) = x_0 \in M,$$ (t) = f(x(t)) + u(t)g(x(t)),x(0) =x 0 ∈ M, wheref andg are real-analytic vector fields onM which are linearly independent at some point ofM, andu is a real-valued control. Sufficient conditions on the vector fieldsf andg are given so that the system is controllable fromx 0. Suppose that every nontrivial integral curve ofg has a pointp wheref andg are linearly dependent,g(p) is nonzero, and that the Lie bracket [f,g] andg are linearly independent atp. Then the system is controllable (with the possible exception of a closed, nowhere dense set which is not reachable) from any pointx 0 such that the vector space dimension of the Lie algebraL A generated byf,g and successive Lie brackets is 2 atx 0.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01744306
