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
Received July 8, 2024
Revised July 26, 2024
Accepted July 29, 2024
Sergey Mironovich Aseev, Dr. Phys.-Math. Sci., Corresponding Member of RAS, Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, 119991 Russia, e-mail: aseev@mi-ras.ru
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Cite this article as: S.M. Aseev. An optimal control problem with a relaxed state constraint. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2024, vol. 30, no. 3, pp. 14–29.
