Second-order conditions for bang-singular extremals

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

Santiago de Chile

Conferencia; ICCOPT 2010; 2010

Mathematical Optimization Society

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 transformed critical directions. Under a certain decoupling assumption (always satisfied in the case of a scalar control), we obtain a characterization of quadratic growth.