Geodesic
Weakening State Constraints in Optimal Control Problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Dynamical Systems, Tome 321 (2023), pp. 31-44

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An optimal control problem is considered in which the integral term of the functional to be minimized contains the characteristic function of a given open set of undesirable system states. The statement of this problem can be viewed as a weakening of the statement of the standard optimal control problem with a state constraint. Conditions are obtained that guarantee the equivalence of these problems. Two illustrative examples are given.
Keywords: optimal control, state constraint, risk zone, differential inclusion. 
@article{TM_2023_321_a1,
     author = {S. M. Aseev},
     title = {Weakening {State} {Constraints} in {Optimal} {Control} {Problems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {31--44},
     publisher = {mathdoc},
     volume = {321},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2023_321_a1/}
}
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S. M. Aseev. Weakening State Constraints in Optimal Control Problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Dynamical Systems, Tome 321 (2023), pp. 31-44. http://geodesic.mathdoc.fr/item/TM_2023_321_a1/