On Normality of Lagrange Multipliers for State Constrained Optimal Control Problems

An optimal control problem for nonlinear ODEs, subject to mixed control-state and pure state constraints is considered. Sufficient conditions are formulated, under which unique normal Lagrange multipliers exist and are given by regular functions. These conditions include pointwise linear independence of gradients of f -active constraints and controllability of the linearized state equation. Under some additional assumptions, further regularity of the multipliers is shown.