The degeneracy phenomenon in optimal control problems with state contraints

We present the complete investigation of the degeneracy phenomenon. We obtain the new version of Pontryagin´s maximum principle for problems with state constraints. This maximum principle contains some additional information about the behavior of the Hamiltonian (maximum function): the new jump conditions at the endtimes. It turns out that these jump conditions at the endtimes are the crucial ones in the investigation of the degeneracy phenomenon. Using this result under some natural controllability conditions we obtain the necessary and sufficient conditions for the maximum principle to be informative