Second order conditions for bang-singular extremals

ARONNA, MARÍA SOLEDAD; BONNANS, J. FRÉDÉRIC; DMITRUK, ANDREI; LOTITO, PABLO ANDRÉS

Santiago

Congreso; International conference on continuous optimization (ICCOPT); 2010

We  consider  an  optimal  control  problem  whose Hamiltonian  function  is  affine  w.r.t.    the  (vector) control  variable.    The  initial  and  final  states  are constrained  by  a  finite  number  of  equalities  and inequalities, and the control has to be nonnegative.Extending the Goh transformation technique to this setting, we are able to derive second-order necessary conditions  expressed  in  terms  of  the  transformedcritical  directions. Under  a  certain  decoupling assumption (always satisfied in the case of a scalar control),  we obtain a characterization of quadratic growth.