An example of a normal control problem with state constraints
The question of the normality of known necessary optimality conditions in the form of Pontryagin’s maximum principle for an optimal control problem with state constraints is investigated. Normality means the positivity of the Lagrange multiplier A0 next to the functional being minimized. An example of a class of control problems is constructed in which the normality of the maximum principle can be guaranteed. The controllability property of the trajectory in the vicinity of any extremal for the indicated class of problems is also noted.