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On Application of Gaussian Functions for Numerical Solution of Optimal Control Problems

  • Nonlinear Systems
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Abstract

It is proved that the linear combinations of shifts and contractions of the Gaussian function can be used for an arbitrarily accurate approximation in the space of continuous functions of one variable on any fixed intervals. On the example of the soft lunar landing problem, a method for the numerical solution of optimal control problems based on this approximation procedure of the control function is described. Within the framework of the same example, the sensitivity of constraint functionals to the specification error of optimal parameters is investigated using three approaches as follows: 1) Pontryagin’s maximum principle (both numerically and theoretically); 2) the control parametrization technique in combination with the method of sliding nodes; 3) the newly proposed method. A comparative analysis is performed that confirms the effectiveness of the third method.

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Acknowledgments

This work was supported by the Ministry of Education and Science of the Russian Federation within the State order for research in 2014–2016, project no. 1727.

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Authors and Affiliations

  1. Lobachevsky Nizhny Novgorod State University, Nizhny Novgorod, Russia

    A. V. Chernov

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  1. A. V. Chernov
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Correspondence to A. V. Chernov.

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Russian Text © The Author(s), 2019, published in Avtomatika i Telemekhanika, 2019, No. 6, pp. 51–69.

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Chernov, A.V. On Application of Gaussian Functions for Numerical Solution of Optimal Control Problems. Autom Remote Control 80, 1026–1040 (2019). https://doi.org/10.1134/S0005117919060031

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