Section: New Results

Second order analysis of deterministic optimal control problems

Participant : Frédéric Bonnans.

F. Bonnans, with M.S. Aronna (IMPA, Rio de Janeiro) and B.-S. Goh (Curtin U., Miri, Sarawak, Malaysia) obtained in [32] new second order necessary and sufficient optimality conditions for a class of control-affine problems with a scalar control and a scalar state constraint. These optimality conditions extend to the constrained state framework the Goh transform, which is the classical tool for obtaining an extension of the Legendre condition. We propose a shooting algorithm to solve numerically this class of problems and we provide a sufficient condition for its local convergence. We provide examples to illustrate the theory. An article by F. Bonnans, X. Dupuis (Ceremade, U. Dauphine) and L. Pfeiffer (U. Graz) has been published in the SIAM J. Control Optim. on “Second-order necessary conditions in Pontryagin form for optimal control problems” [16] .