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A Numerical Method for Finding the Optimal Solution of a Differential Inclusion

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An Erratum to this article was published on 01 October 2019

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Abstract

In the paper, we study a differential inclusion with a given continuous convex multivalued mapping. For a prescribed finite time interval, it is required to construct a solution to the differential inclusion, which satisfies the prescribed initial and final conditions and minimizes the integral functional. By means of support functions, the original problem is reduced to minimizing some functional in the space of partially continuous functions. When the support function of the multivalued mapping is continuously differentiable with respect to the phase variables, this functional is Gateaux differentiable. In the study, the Gateaux gradient is determined and the necessary conditions for the minimum of the functional are obtained. Based on these conditions, the method of steepest descent is applied to the original problem. The numerical examples illustrate the implementation of the constructed algorithm.

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  • 23 December 2019

    erratum

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, 199034, Russia

    A. V. Fominyh

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  1. A. V. Fominyh
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Correspondence to A. V. Fominyh.

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Original Russian Text © A.V. Fominyh, 2018, published in Vestnik Sankt-Peterburgskogo Universiteta: Matematika, Mekhanika, Astronomiya, 2018, Vol. 51, No. 4, pp. 645–657.

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Fominyh, A.V. A Numerical Method for Finding the Optimal Solution of a Differential Inclusion. Vestnik St.Petersb. Univ.Math. 51, 397–406 (2018). https://doi.org/10.3103/S1063454118040076

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