Local Minimum Principle for Optimal Control Problems with Mixed Constraints: the Nonregular Caseстатья
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Дата последнего поиска статьи во внешних источниках: 19 июня 2024 г.
Аннотация:We consider an optimal control problemwith a finite number ofmixed constraints Gi(x,u) ≤ 0 that are nonregular, i.e. when the gradientsG′iu(x,u) of active constraints can be positively dependent at some points of the reference process. All data of the problemare assumed to besmooth. UsingtheDubovitskii–Milyutin theoremon the approximative separation of convexcones, we prove first order necessary conditionfor aweakminimumin the formof so-called “localminimumprinciple”, which is formulated in terms of integrable functions and Lebesgue–Stieltjes measures, without usingfunctionals from(L∞)∗ . Some illustrative examples are given. Thework is based on Milyutin’s book(MaximumPrinciple in theGeneral Problemof OptimalControl. Fizmatlit,Moscow, 2001) and is an extension of our paper Dmitruk andOsmolovskii (SIAMJ. ControlOptim. 60(4):1919-1941 ,2022) that admits only onemixed inequality constraint.https://doi.org/10.1007/s00245-023-09993-1