Geodesic
An optimal control problem with a relaxed state constraint
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 3, pp. 14-29 Cet article a éte moissonné depuis la source Math-Net.Ru

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We explore an optimal control problem in the context of a specified open set representing “undesirable” system states. This problem statement is closely linked to the standard optimal control problem with a state constraint and can be viewed as a relaxation of the latter. The interrelation between these problems is examined. The recently derived necessary first-order optimality conditions for the discussed problem are presented. Additionally, an illustrative example is given.
Keywords: optimal control, differential inclusion, Pontryagin's maximum principle, refined Euler–Lagrange inclusion, state constraint, discontinuous integrand, risk zone. 
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S. M. Aseev. An optimal control problem with a relaxed state constraint. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 3, pp. 14-29. http://geodesic.mathdoc.fr/item/TIMM_2024_30_3_a1/

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