# American Institute of Mathematical Sciences

December  2006, 5(4): 861-885. doi: 10.3934/cpaa.2006.5.861

## Second order conditions for the controllability of nonlinear systems with drift

 1 Dipartimento di Matematica Pura e Applicata, Università di Padova, via Belzoni 7, 35131 Padova, Italy

Received  November 2005 Revised  May 2006 Published  September 2006

In this paper we study controllability of control systems in $\mathbb R^n$ of the form $\dot x=f(x)+\sum_{i=1}^m$ $u_ig_i(x)$ with $u\in\mathcal U$ compact convex subset of $\mathbb R^n$ with a rather general target. The symmetric (driftless) case, i.e. $f=0$, is a very classical topic, and in this case the results on controllability and Hölder continuity of the minimal time function $T$ are related to certain properties of the Lie algebra generated by the $g_i$'s. Here, we want to extend some results on controllability and Hölder continuity of $T$ to some cases where $f\ne 0$.
Citation: Antonio Marigonda. Second order conditions for the controllability of nonlinear systems with drift. Communications on Pure & Applied Analysis, 2006, 5 (4) : 861-885. doi: 10.3934/cpaa.2006.5.861
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