# American Institute of Mathematical Sciences

June  2013, 3(2): 185-208. doi: 10.3934/mcrf.2013.3.185

## Time optimal control for a nonholonomic system with state constraint

 1 Université de Lorraine, Institut Elie Cartan de Lorraine, UMR 7502, Vandoeuvre-lès-Nancy, F-54506, France, France

Received  June 2012 Revised  December 2012 Published  March 2013

The aim of this paper is to tackle the time optimal controllability of an $(n+1)$-dimensional nonholonomic integrator. In the optimal control problem we consider, the state variables are subject to a bound constraint. We give a full description of the optimal control and optimal trajectories are explicitly obtained. The optimal trajectories we construct, lie in a 2-dimensional plane and they are composed of arcs of circle.
Citation: Jérome Lohéac, Jean-François Scheid. Time optimal control for a nonholonomic system with state constraint. Mathematical Control & Related Fields, 2013, 3 (2) : 185-208. doi: 10.3934/mcrf.2013.3.185
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