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Methods of Numerical Solution of Optimal Control Problems Based on the Pontryagin Maximum Principle

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Abstract

In this paper, we study optimal control problems whose behavior is described by second-order differential equations with nonlocal Bitsadze–Samarski boundary conditions. Necessary conditions of optimality are obtained in terms of the maximum principle; adjoint equations are constructed in the differential and integral form. Necessary and sufficient optimality conditions are obtained for a linear problem, a difference scheme is constructed and examined, and a numerical algorithm is proposed.

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Authors and Affiliations

  1. Shota Rustaveli Batumi State University, Batumi, Georgia

    D. Devadze & V. Beridze

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  1. D. Devadze
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  2. V. Beridze
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Correspondence to D. Devadze.

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 89, Differential Equations and Mathematical Physics, 2013.

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Devadze, D., Beridze, V. Methods of Numerical Solution of Optimal Control Problems Based on the Pontryagin Maximum Principle. J Math Sci 206, 348–356 (2015). https://doi.org/10.1007/s10958-015-2316-6

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  • DOI: https://doi.org/10.1007/s10958-015-2316-6

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