On second-order optimality conditions in optimal control

We observe some results obtained by the author on necessary and sufficient second-order conditions for the strong, bounded strong, Pontryagin's and weak local minimum in optimal control problems with control system, given by ordinary differential equations, considered on a fixed time interval, subject to control constraints and finite number of end-point constraints of equality and inequality type. We assume that the control constraints are given by a finite number of inequalities with linearly independent gradients of active constraints.