A canonical expansion for nonlinear systems. (English) Zbl 0618.93028

Su, Renjeng; Hunt, L. R.

IEEE Trans. Autom. Control 31, 670-673 (1986).

In the first part of the paper the authors consider n vector fields \(X_ 1,...,X_ n\) which are linear independent and analytic in a neighborhood of the origin of \({\mathbb{R}}^ n\). A local coordinate system based on \(X_ 1,...,X_ n\) is constructed, and it is shown that in this coordinate system each analytic vector field has a series expansion whose coefficients are computed in terms of Lie brackets.
In the second part, the authors apply this result to control systems of the form \[ \dot x=f(x)+\sum^{m}_{i=1}g_ i(x)u_ i \] which satisfy suitable assumptions. The resulting expansion allows us to find out the feedback linearizable part of the given system.

Reviewer: A.Bacciotti

MSC:

93C10	Nonlinear systems in control theory
57R27	Controllability of vector fields on \(C^\infty\) and real-analytic manifolds
93B27	Geometric methods
41A58	Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
93C15	Control/observation systems governed by ordinary differential equations

Keywords:

vector fields; series expansion; Lie brackets