Sufficient quadratic conditions of extremum for discontinuous controls in optimal control problems with mixed constraints

We derive second-order sufficient optimality conditions for discontinuous controls in optimal control problems of ordinary differential equations with initial-final state constraints and mixed state-control constraints of equality and inequality type. Under the assumption that the gradients with respect to the control of active mixed constraints are linearly independent, the sufficient conditions imply a bounded strong minimum in the problem. © 2011 Springer Science+Business Media, Inc.