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Application of the hypodifferential descent method to the problem of constructing an optimal control

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Abstract

In this paper the problem of optimal control of a nonlinear ODE system with given boundary conditions and the integral restriction on control is considered. With the help of the theory of exact penalty functions the original problem is reduced to the problem of unconstrained minimization of a nonsmooth functional. The necessary minimum conditions in terms of hypodifferentials are found. A class of problems for which these conditions are also sufficient is distinguished. On the basis of these conditions the hypodifferential descent method is applied to the considered problem. Under some additional assumptions the hypodifferential descent method converges in a certain sense.

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Acknowledgements

This work was supported by Russian Fund of Fundamental Research, Project No. 16-31-00056 mol-a.

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Authors and Affiliations

  1. St. Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, Russia, 199034

    A. V. Fominyh, V. V. Karelin & L. N. Polyakova

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  1. A. V. Fominyh
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  2. V. V. Karelin
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  3. L. N. Polyakova
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Correspondence to A. V. Fominyh.

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Fominyh, A.V., Karelin, V.V. & Polyakova, L.N. Application of the hypodifferential descent method to the problem of constructing an optimal control. Optim Lett 12, 1825–1839 (2018). https://doi.org/10.1007/s11590-017-1222-x

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  • DOI: https://doi.org/10.1007/s11590-017-1222-x

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