Stability and Sensitivity Analysis for Optimal Control Problems with a First-Order State Constraint and Application to Continuation Methods

This talk deals with stability and sensitivity analysis for optimal control problems of an ordinary differential equation with a first-order state constraint. We consider the case when the Hamiltonian and the state constraint are regular. Malanowski (2) obtained Lipschitz continuity and directional differentiability of solutions in L, using generalized implicit functions theorems in infinite dimensional spaces, and without any assumptions on the structure of the trajectory. Malanowski and Maurer (3) proved that the solution and multipliers are C with respect to the parameter by application of the implicit function theorem to the shooting mapping, when there are finitely many junction times and strict complementarity holds. Under those assumptions the structure of the perturbed solutions is stable.