Abstract
We consider a nonlinear optimal control problem with an integral functional in which the integrand is the characteristic function of a closed set in the phase space. An approximation method is applied to prove the necessary conditions of optimality in the form of a Pontryagin maximum principle without any prior assumptions on the behavior of the optimal trajectory. Similarly to phase-constrained problems, we derive conditions of nondegeneracy and pointwise nontriviality of the maximum principle.
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Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 179–204, 2004.
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Aseev, S.M., Smirnov, A.I. Necessary first-order conditions for optimal crossing of a given region. Comput Math Model 18, 397–419 (2007). https://doi.org/10.1007/s10598-007-0034-8
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DOI: https://doi.org/10.1007/s10598-007-0034-8