Investigation of the degeneracy phenomenon of the maximum principle for optimal control problems with state constraints

In this paper we study the degeneracy phenomenon in optimal control problems with state constraints. It is shown that this phenomenon occurs because of the incompleteness of the standard variants of Pontryagin's maximum principle for problems with state constraints. A new maximum principle containing additional information about the behavior of the Hamiltonian at the endtimes is developed. We also obtain some sufficient and necessary conditions for nondegeneracy and pointwise nontriviality of the maximum principle. The results obtained pertain to optimal control problems with systems described by differential inclusions and ordinary differential equations.