Degeneracy phenomenon in optimal control problems with state constraints

The degeneracy phenomenon in optimal control systems is investigated. The new version of Pontryagin's maximum principle for problems with state constraints is obtained. This maximum principle contains some additional information about the behavior of the Hamiltonian. The jump conditions at the endtimes are important in the investigation of the degeneracy phenomenon. Using this result under some natural controllability conditions, the necessary and sufficient conditions for the maximum principle to be informative is obtained.