an:01584877
Zbl 1127.93334
Pommaret, Jean-Fran??ois
Controllability of nonlinear multidimensional control systems
EN
Isidori, Alberto (ed.) et al., Nonlinear control in the year 2000. Vol. 2. London: Springer (ISBN 1-85233-364-2). Lect. Notes Control Inf. Sci. 259, 245-255 (2001).
2001
a
93C10 93B15 93B20 93C20
controllability; nonlinear systems; differential modules; multidimensional systems
Summary: It is now known that the controllability of a linear multidimensional control system is a structural property equivalent to the lack of torsion of the corresponding differential module and can be tested, even in the case of nonconstant coefficients. It is therefore tempting to decide about the controllability of a nonlinear control system through the controllability of its generic linearization. The main purpose of this paper is to answer this question negatively, in general, by presenting for the first time the counterexample of a nonlinear system which is controllable while its generic linearization is not controllable. We also provide a test for searching autonomous observables, extending the one already existing in the 1-dimensional case.
For the entire collection see [Zbl 0953.00023].