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Constructing the set of program controls with probability 1 for one class of stochastic systems

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Abstract

The definitions of the program control for stochastic systems were traditionally constructed for the integral manifolds with time-independent equations. The presented approach takes into account the dynamism, time-to-time variability, of the invariance surface. A program control enabling the given dynamic stochastic system to remain within the given manifold was constructed, and an example was given.

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References

  1. Dubko, V.A., First Integral of the System of Stochastic Differential Equations, Preprint of the Kiev Mat. Inst., USSR Acad. Sci., Kiev, 1978.

  2. Dubko, V.A., Integral Invariants for One Class of Systems of Stochastic Differential Equations, Dokl. Akad. Nauk SSSR, 1984, no. 1, ser. A, pp. 18–21.

  3. Dubko, V.A., Voprosy teorii i primeneniya stokhasticheskikh differentsial’nykh uravnenii (Problems of Theory and Application of Stochastic Differential Equations), Vladivostok: Akad. Nauk SSSR, 1989.

    Google Scholar 

  4. Dubko, V.A., Open Evolving Systems (Some Aspects of Mathematical Modeling), in Persha mizhnarodna naukovo-praktichna konferentsiya “Vidkriti evolyutsionuyuchsh sistemi” (Dodatok), Sb. tekstov dokl. (First Int. Conf. “Open Evolving Systems”), Application, Collected Papers), Kiev: VNZ VMURoL, 2002, pp. 14–31.

    Google Scholar 

  5. Dubko, V.A., V poiskakh skrytogo poryadka (In Quest of Hidden Order), Vladivostok: Dal’nauka, 1995.

    Google Scholar 

  6. Dubko, V.A. and Chalykh, E.V., Brownian Motion with Deterministic Velocity Magnitude, Preprint of Kiev Mat. Inst., NAN Ukraine, 1997.

  7. Dubko, V.A. and Chalykh, E.V., Construction of Analytical Solution for One Class of Langevin Equations with Random Orthogonal Actions, Ukr. Mat. Zh., 1998, vol. 50, no. 4, pp. 604–605.

    Article  MathSciNet  Google Scholar 

  8. Chalykh, E.V., On One Generalization of the Langevin Equations with Deterministic Velocity Magnitude, Ukr. Mat. Zh., 1998, vol. 50, no. 5, pp. 712–713.

    Google Scholar 

  9. Chalykh, E.V., Construction of a Diffusion Approximation of the Position of a Brownian Particle with Orthogonal Actions, Preprint of Inst. Appl. Mat., Khabarovsk: Ross. Akad. Nauk, 1998.

    Google Scholar 

  10. Chalykh, E.V., Availability of Conserved Functionals of Brownian Motion in Random Environment, Preprint of Inst. Appl. Mat., Khabarovsk: Ross. Akad. Nauk, 1998.

    Google Scholar 

  11. Chalykh, E.V., Program Control with Probability 1 for Open Systems, Obozr. Prikl. Prom. Mat., 2007, vol. 14, no. 2, pp. 253–254.

    MathSciNet  Google Scholar 

  12. Chalykh, E.V., Program Control for Open Systems. Ecologo-Geographic Problems of Nature Management of Oil-and-Gas Regions: Theory, Methods, Practice, in Dokl. III mezhdunar. nauch.-prakt. konf. (Nizhnevartovsk, 25–27 oktyabrya 2006), 2-e dopolnennoe izd. (Proc. III Int. Conf. (Nizhnevartovsk, October 25–27, 2006), Second Supplemented Ed.), Nizhnevartovsk: Nizhnevart. State Human. Univ., 2007, pp. 122–125.

    Google Scholar 

  13. Galiullin, A.S., Mukhametzyanov, I.A., Mukharlyamov, R.G., and Furasov, V.D., Postroenie sistem programmnogo dvizheniya (Construction of Program Motion Systems), Moscow: Nauka, 1971.

    MATH  Google Scholar 

  14. Gikhman, I.I. and Skorokhod, A.V., Stokhasticheskie differentsial’nye uravneniya (Stochastic differential equations), Kiev: Naukova Dumka, 1968.

    Google Scholar 

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Original Russian Text © E.V. Chalykh, 2009, published in Avtomatika i Telemekhanika, 2009, No. 8, pp. 110–122.

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Chalykh, E.V. Constructing the set of program controls with probability 1 for one class of stochastic systems. Autom Remote Control 70, 1364–1375 (2009). https://doi.org/10.1134/S0005117909080098

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