Second order necessary conditions for optimal control problems with control and integral constraints

An optimal control problem containing restrictions on control variables and integral equality and inequality constraints is considered. A relatively simple and self-contained method for deriving new second order necessary conditions for such problems is presented. The new conditions derived here generalize some of the results reported in [3], [6], [9]. The method developed is quite general and is also applicable to optimal control problems including state or mixed state-control inequality constraints and to optimal control problems governed by partial differential equations.