6533b7dcfe1ef96bd1272952
RESEARCH PRODUCT
Second order optimality conditions in the smooth case and applications in optimal control
Bernard BonnardEmmanuel TrélatJean-baptiste Caillausubject
[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologyMathematical optimizationControl and Optimization02 engineering and technology01 natural sciences020901 industrial engineering & automationJacobi fieldSingularity0101 mathematicsorbit transferMathematicsSecond derivativeJacobi fieldsecond-order intrinsic derivative010102 general mathematicsConjugate pointsattitude control49K15 49-04 70Q05[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Optimal controlComputational MathematicsFlow (mathematics)Control and Systems EngineeringTrajectoryconjugate pointLagrangian singularity[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Orbit (control theory)description
International audience; The aim of this article is to present algorithms to compute the first conjugate time along a smooth extremal curve, where the trajectory ceases to be optimal. It is based on recent theoretical developments of geometric optimal control, and the article contains a review of second order optimality conditions. The computations are related to a test of positivity of the intrinsic second order derivative or a test of singularity of the extremal flow. We derive an algorithm called COTCOT (Conditions of Order Two and COnjugate times), available on the web, and apply it to the minimal time problem of orbit transfer, and to the attitude control problem of a rigid spacecraft. This algorithm involves both normal and abnormal cases.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2007-04-01 |