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State constraints in optimal control. The degeneracy phenomenon. (English) Zbl 0873.49015
Summary: We study the degeneracy phenomenon arising 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. The new maximum principle containing some additional information about the behavior of the Hamiltonian at the endtimes is developed. As application we obtain some sufficient and necessary conditions for nondegeneracy and pointwise nontriviality of the maximum principle. The results obtained include the optimal control problems of systems described by differential inclusions and ordinary differential equations.

49K15 Optimality conditions for problems involving ordinary differential equations
49J24 Optimal control problems with differential inclusions (existence) (MSC2000)
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