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On Two-Sided Approximations of Reachable Sets of Control Systems with Geometric Constraints on the Controls

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Abstract

We consider a nonlinear control system in Euclidean space on a finite time interval with controls subject to geometric constraints. The question of constructing lower and upper (by inclusion) approximations of reachable sets of this system is studied. Under certain conditions, estimates are obtained for the discrepancy (in the Hausdorff metric) between the lower and upper approximations of the reachable sets.

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Funding

This work was supported by the Russian Foundation for Basic Research (project nos. 18-01-00264 and 18-01-00221).

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 620108, Yekaterinburg, Russia

    V. N. Ushakov & M. V. Pershakov

Authors
  1. V. N. Ushakov
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  2. M. V. Pershakov
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Correspondence to V. N. Ushakov or M. V. Pershakov.

Additional information

Translated from Trudy Instituta Matematiki i Mekhaniki UrO RAN, Vol. 26, No. 1, pp. 239 - 255, 2020 https://doi.org/10.21538/0134-4889-2020-26-1-239-255.

Translated by I. Tselishcheva

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Ushakov, V.N., Pershakov, M.V. On Two-Sided Approximations of Reachable Sets of Control Systems with Geometric Constraints on the Controls. Proc. Steklov Inst. Math. 313 (Suppl 1), S211–S227 (2021). https://doi.org/10.1134/S0081543821030226

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