6533b828fe1ef96bd1288e1b
RESEARCH PRODUCT
Asymptotics of accessibility sets along an abnormal trajectory
Emmanuel Trélatsubject
[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologyControl and OptimizationOptimization problemRank (linear algebra)02 engineering and technologycontrol-affine systems01 natural sciencesSet (abstract data type)020901 industrial engineering & automationFOS: Mathematicssingular trajectories0101 mathematicsMathematics - Optimization and ControlMathematics010102 general mathematicsMathematical analysisConstraint (information theory)Computational MathematicsCone (topology)Optimization and Control (math.OC)Control and Systems EngineeringControl systemTrajectoryAffine transformation[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]description
We describe precisely, under generic conditions, the contact of the accessibility set at time $T$ with an abnormal direction, first for a single-input affine control system with constraint on the control, and then as an application for a sub-Riemannian system of rank 2. As a consequence we obtain in sub-Riemannian geometry a new splitting-up of the sphere near an abnormal minimizer $\gamma$ into two sectors, bordered by the first Pontryagin's cone along $\gamma$, called the $\xLinfty$-sector and the $\xLtwo$-sector. Moreover we find again necessary and sufficient conditions of optimality of an abnormal trajectory for such systems, for any optimization problem.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2001-01-01 |