EQUIVARIANT MOVING FRAME METHOD AND THE LOCAL EQUIVALENCE OF u(xx) = r(x, u, v, u(x), v(x)) UNDER FIBER-PRESERVING TRANSFORMATIONS

作者：Valiquette F^*

来源：Journal of Dynamical and Control Systems, 2011, 17(4): 555-589.

DOI：10.1007/s10883-011-9130-3

• Control systems
• differential invariants
• equivalence problems
• equivariant moving frames
• Maurer-Cartan forms

We use the equivariant moving frame method to study the local equivalence problem of scalar control equations of the form u(xx) = r(x, u, v, u(x), v(x)) under the pseudo-group of fiber-preserving transformations X = phi(x), U = beta(x, u), V = alpha(x, u, v). Three typical branches of the equivalence problem are considered: the degenerate case, which contains the control systems with largest fiber-preserving symmetry group, the branch containing the Hilbert-Cartan equation, and the generic case.

• 出版日期2011-9