Time optimal control for a nonholonomic system with state constraint
Jérome Lohéac Jean-François Scheid
Mathematical Control & Related Fields 2013, 3(2): 185-208 doi: 10.3934/mcrf.2013.3.185
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.
keywords: state constraints. Pontryagin's maximum principle Nonholonomic integrator time optimal control controllability

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