A Second-Order Maximum Principle in Optimal Control Under State Constraints
A second-order variational inclusion for control systems under state constraints is derived and applied to investigate necessary optimality conditions for the Mayer optimal control problem. A new pointwise condition verified by the adjoint state of the maximum principle is obtained as well as a second-order necessary optimality condition in the integral form. Finally, a new sufficient condition for normality of the maximum principle is proposed. Some extensions to the Mayer optimization problem...