Geometric methods in linearization of control systems
Simple germs of corank one affine distributions
Phase portraits of planar control-affine systems
Flat outputs of two-input driftless control systems
We study the problem of flatness of two-input driftless control systems. Although a characterization of flat systems of that class is known, the problems of describing all flat outputs and of calculating them is open and we solve it in the paper. We show that all -flat outputs are parameterized by an arbitrary function of three canonically defined variables. We also construct a system of 1st order PDE’s whose solutions give all -flat outputs of two-input driftless systems. We illustrate our results...
Flat outputs of two-input driftless control systems
We study the problem of flatness of two-input driftless control systems. Although a characterization of flat systems of that class is known, the problems of describing all flat outputs and of calculating them is open and we solve it in the paper. We show that all -flat outputs are parameterized by an arbitrary function of three canonically defined variables. We also construct a system of 1st order PDE’s whose solutions give all -flat outputs of two-input...
On the geometry of Goursat structures
A Goursat structure on a manifold of dimension is a rank two distribution such that dim , for , where denote the elements of the derived flag of , defined by and . Goursat structures appeared first in the work of von Weber and Cartan, who have shown that on an open and dense subset they can be converted into the so-called Goursat normal form. Later, Goursat structures have been studied by Kumpera and Ruiz. In the paper, we introduce a new local invariant for Goursat structures, called...
On the Geometry of Goursat Structures
A Goursat structure on a manifold of dimension is a rank two distribution such that dim = + 2, for 0 ≤ ≤ -2, where denote the elements of the derived flag of , defined by = and = + [ , ] . Goursat structures appeared first in the work of von Weber and Cartan, who have shown that on an open and dense subset they can be converted into the so-called Goursat normal form. Later, Goursat...
Flat outputs of two-input driftless control systems
We study the problem of flatness of two-input driftless control systems. Although a characterization of flat systems of that class is known, the problems of describing all flat outputs and of calculating them is open and we solve it in the paper. We show that all -flat outputs are parameterized by an arbitrary function of three canonically defined variables. We also construct a system of 1st order PDE’s whose solutions give all -flat outputs of two-input...
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