Global controllability of nonlinear systems in two dimensions |
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Authors: | L. R. Hunt |
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Affiliation: | (1) Department of Mathematics, Texas Tech University, 79409 Lubbock, Texas, USA |
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Abstract: | LetM be a connected real-analytic 2-dimensional manifold. Consider the system (t) = f(x(t)) + u(t)g(x(t)),x(0) =x0 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 fromx0. 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 pointx0 such that the vector space dimension of the Lie algebraLA generated byf,g and successive Lie brackets is 2 atx0.Research supported in part by the National Science Foundation under NSF Grant MCS76-05267-A01 and by the Joint Services Electronics Program under ONR Contract 76-C-1136. |
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