A classification of generic families of control-affine systems and their bifurcations |
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Authors: | Marek W. Rupniewski Witold Respondek |
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Affiliation: | (1) Department of Mathematics, Rutgers University, New Brunswick, USA; |
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Abstract: | We study control-affine systems with n − 1 inputs evolving on an n-dimensional manifold for which the distribution spanned by the control vector fields is involutive and of constant rank (equivalently, they may be considered as 1-dimensional systems with n − 1 inputs entering nonlinearly). We provide a complete classification of such generic systems and their one-parameter families. We show that a generic family for n > 2 is equivalent (with respect to feedback or orbital feedback transformations) to one of nine canonical forms which differ from those for n = 2 by quadratic terms only. We also describe all generic bifurcations of 1-parameter families of systems of the above form. |
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