The Euler approximation in state constrained optimal control

We analyze the Euler approximation to a state constrained control problem. We show that if the active constraints satisfy an independence condition an d the Lagrangian satisfies a coercivity condition, then locally there exist s a solution to the Euler discretization, and the error is bounded by a con stant times the mesh size. The proof couples recent stability results for s tate constrained control problems with results established here on discrete -time regularity. The analysis utilizes mappings of the discrete variables into continuous spaces where classical finite element estimates can be invo ked.