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Second order optimality conditions with applications

Pages: 145 - 154, Issue Special, September 2007

 Abstract        Full Text (3711.1K)              

B. Bonnard - Institut de Mathématiques, Université de Bourgogne, 21078 Dijon, France (email)
J.-B. Caillau - ENSEEIHT-IRIT (UMR CNRS 5505), Institut National Polytechnique de Toulouse, 31071 Toulouse, France (email)
E. Trélat - Laboratoire MAPMO (UMR CNRS 6628), Université d'Orléans, 45067 Orléans, France (email)

Abstract: An algorithm to compute the first conjugate point along a smooth extremal curve is presented. Under generic assumptions, the trajectory ceases to be locally optimal at such a point. An implementation of this algorithm, called cotcot, is available online and based on recent developments in geometric optimal control. It is applied to analyze the averaged optimal transfer of a satellite between elliptic orbits.

Keywords:  Orbital transfer, time optimal control, Riemannian systems with drift, conjugate points.
Mathematics Subject Classification:  49K15, 70Q05.

Received: August 2006;      Revised: March 2007;      Published: September 2007.