Abstract
In this paper, first order necessary conditions of optimality for control problems with pathwise state constraints are provided. These conditions are able to avoid the degeneracy phenomenon which affects standard versions of the maximum principle. A common feature of the endpoint degeneracy phenomena described in the literature is identified and it is shown that similar phenomena might occur other than at the endpoints of the trajectory. A strengthened form of the maximum principle is established under suitable constraint qualifications, in which the (measure) multiplier associated with the pathwise state constraint is not involved in the nontriviality condition.
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