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Choosing the sequence of approach of a nonlinear object to a group of moving points

  • Optimal Control
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Abstract

The problem of the fastest sequential approach of a controlled object, described by a nonlinear third-order system, to a group of points is considered. The necessary condition of the approach sequence optimality is obtained. Examples are given.

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References

  1. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1983; Gordon and Breach, New York, 1986).

    MATH  Google Scholar 

  2. N. N. Krasovskii, Motion Control Theory (Nauka, Moscow, 1968) [in Russian].

    Google Scholar 

  3. Yu. I. Berdyshev, “To a Problem of Successive Approach of a Third-Order Nonlinear Control System to a Group of Moving Points,” Prikl. Mat. Mekh. 66(5) (2002).

  4. Yu. I. Berdyshev, “To a Problem of Consecutive Traversal of Two Moving Points by a Nonlinear Object,” in Proceedings of Institute of Mathematics and Mechanics of Ural Division of RAS (Yekaterinburg, 2005), Vol. 11 [in Russian].

  5. Yu. I. Berdyshev, “On a Nonlinear Problem of a Sequential Control with a Parameter,” Izv. Ross. Akad. Nauk, Teor. Sist. Upr., No. 3, (2008) [Comp. Syst. Sci. 47 (3), 380–385 (2008)].

  6. Yu. I. Berdyshev and A. G. Chentsov, “Optimization of the External Criterion in a Control Problem,” Kibernetika, No. 1 (1986).

  7. S. I. Morina and A. G. Chentsov, The Problem of Successive Approach under Combined Constraints on the Choice of a Control, Available from VINITI, No. 6461-B87 (Sverdlovsk, 1987) [in Russian].

  8. R. Isaacs, Differential Games (Wiley, New York, 1965; Mir, Moscow, 1967).

    MATH  Google Scholar 

  9. R. Bellman, “Application of Dynamic Programming to Travelling Salesman Problem,” in Kiberneticheskii Sbornik (Mir, Moscow, 1964), Vol. 9 [in Russian].

    Google Scholar 

  10. L. N. Korotaeva, A. N. Sesekin, and A. G. Chentsov, “To a Modification of the Dynamic Programming Method in the Problem of Succesive Approach,” Zh. Vychisl. Mat. Mat. Fiz. 29(8) (1989).

  11. I. I. Melamed and S. I. Sergeev, “Travelling Salesman Problem. Theoretical Problems,” Avtom. Telemekh., No. 1 (1989).

  12. A. G. Chentsov, “Extremal Routing and Task Allocation Problems: Theoretical Problems” in Regular and Chaotic Dynamics (Moscow-Izhevsk, 2008) [in Russian].

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Original Russian Text © Yu.I. Berdyshev, 2011, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2011, No. 1, pp. 32–39.

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Berdyshev, Y.I. Choosing the sequence of approach of a nonlinear object to a group of moving points. J. Comput. Syst. Sci. Int. 50, 30–37 (2011). https://doi.org/10.1134/S1064230711010060

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  • DOI: https://doi.org/10.1134/S1064230711010060

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