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Optimality conditions in problems of control over systems of impulsive differential equations with nonlocal boundary conditions

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Ukrainian Mathematical Journal Aims and scope

We investigate the problem of optimal control in which the state of the controlled system is described by impulsive differential equations with nonlocal boundary conditions, which is a natural generalization of the Cauchy problem. Using the principle of contracting mappings, we prove the existence and uniqueness of a solution of a nonlocal boundary-value problem with impulse perturbations and fixed admissible controls. Under certain conditions for the initial data of the problem, we calculate the gradient of a functional and obtain necessary optimality conditions.

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Authors and Affiliations

  1. Baku State University, Baku, Azerbaijan

    Ya. A. Sharifov

  2. Institute of Cybernetics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan

    Ya. A. Sharifov

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  1. Ya. A. Sharifov
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 6, pp. 836–847, June, 2012.

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Sharifov, Y.A. Optimality conditions in problems of control over systems of impulsive differential equations with nonlocal boundary conditions. Ukr Math J 64, 958–970 (2012). https://doi.org/10.1007/s11253-012-0691-4

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  • DOI: https://doi.org/10.1007/s11253-012-0691-4

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