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Target-Point Interpolation of a Program Control in the Approach Problem

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Abstract

For a nonlinear controlled system, a fixed-time approach problem is considered in which the target point location becomes known only at the start of motion. According to the proposed solution method, node resolving program controls corresponding to a finite collection of target points from the set of their admissible locations are computed in advance and a refined control for the target point given at the start of motion is determined via linear interpolation of the node controls. The procedure for designing such a resolving control is formulated in the form of two algorithms, one of which is run before the start of the motion, and the other is executed in real time while the system is moving. The error in the transfer of the system’s state to the target point by applying these algorithms is estimated. As an example, we consider the approach problem for a modified Dubins car model and a target point about which only a compact set of its admissible locations is known before the start of motion.

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Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

  1. Experimental Machine-Design Bureau “Novator”, 620091, Yekaterinburg, Russia

    A. V. Alekseev

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

    A. A. Ershov

  3. Ural Federal University, 620002, Yekaterinburg, Russia

    A. A. Ershov

Authors
  1. A. V. Alekseev
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  2. A. A. Ershov
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Correspondence to A. V. Alekseev or A. A. Ershov.

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Translated by I. Ruzanova

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Alekseev, A.V., Ershov, A.A. Target-Point Interpolation of a Program Control in the Approach Problem. Comput. Math. and Math. Phys. 64, 585–598 (2024). https://doi.org/10.1134/S0965542524030035

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