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Year 2021, Volume: 10 Issue: 2, 40 - 48, 31.08.2021

Abstract

References

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  • A. Gill, Linear Sequential Machines, Nauka, (Russian), 1975.
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  • R. Gabasov, F. M. Kirillova, E. S. Payasok, Robust Optimal Control on Imperfect Measurements of Dynamic Systems States, Applied and Computational Mathematics, 8(1), (2009), 54-69.
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  • V. Azhmyakov, M. V. Basın, A. E. G. Garcia, Optimal Control Processes Associated with a Class of Discontinuous Control Systems: Applications to Sliding Mode Dynamics, Kybernetika, 50(1), (2014), 5-18.
  • Y. Hacı, M. Candan, On the Principle of Optimality for Linear Stochastic Dynamic System, International Journal in Foundations of Computer Science and Technology. 6(1), (2016), 57-63.
  • Y. Hacı, K. Özen, Terminal Control Problem for Processes Represented by Nonlinear Multi Binary Dynamic System, Control and Cybernetics, 38(3), (2009), 625-633.
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Optimal control processes associated with a class of stochastic sequential dynamical systems based on a parameter

Year 2021, Volume: 10 Issue: 2, 40 - 48, 31.08.2021

Abstract

This paper examines the optimal control processes represented by stochastic sequential dynamic systems involving a parameter obtained by unique solution conditions concerning constant input values. Then, the principle of optimality is proven for the considered process. Afterwards, the Bellman equation is constructed by applying the dynamic programming method. Moreover, a particular set defined as an accessible set is established to show the existence of an optimal control problem. Finally, it is discussed the need for further research.

References

  • B. S. Mordukhovich., Variational Analysis and Generalized Differentiation, I: Basic Theory, Springer, 2013.
  • A. Gill, Linear Sequential Machines, Nauka, (Russian), 1975.
  • I. V. Gaishun, Completely Solvable Multidimensional Differential Equations, Nauka and Tekhnika, Minsk, 1983.
  • Y. M. Yermolyev, Stochastic Programming Methods, Nauka (in Russian), 1976.
  • R. Bellman, Dynamic Programming, Princeton University Press, Princeton, 1957.
  • L. S. Pontryagin, V. G. Boltyanskii, Gamkrelidze, Mishchenko., The Mathematical Theory of Optimal Processes, Interscience Publishers, New York, 1962.
  • V. G. Boltyanskii, Optimal Control of Discrete Systems, John Willey, New York, 1978.
  • R. G. Farajov, Linear Sequential Machines, Sov. Radio, (in Russian), 1975.
  • J. A. Anderson, Discrete Mathematics with Combinatorics, Prentice-Hall, New Jersey, 2004.
  • R. Gabasov, F. M Kirillova, N. S. Paulianok, Optimal Control of Linear Systems on Quadratic Performance Index, Applied and Computational Mathematics, 12(1), (2008), 4-20.
  • R. Gabasov, F. M. Kirillova, E. S. Payasok, Robust Optimal Control on Imperfect Measurements of Dynamic Systems States, Applied and Computational Mathematics, 8(1), (2009), 54-69.
  • J. F. Bonnans, C. S. Fernandez de la Vega, Optimal Control of State Constrained Integral Equations, Set-Valued and Variational Analysis. 18 (3-4), (2010), 307-326.
  • V. Azhmyakov, M. V. Basın, A. E. G. Garcia, Optimal Control Processes Associated with a Class of Discontinuous Control Systems: Applications to Sliding Mode Dynamics, Kybernetika, 50(1), (2014), 5-18.
  • Y. Hacı, M. Candan, On the Principle of Optimality for Linear Stochastic Dynamic System, International Journal in Foundations of Computer Science and Technology. 6(1), (2016), 57-63.
  • Y. Hacı, K. Özen, Terminal Control Problem for Processes Represented by Nonlinear Multi Binary Dynamic System, Control and Cybernetics, 38(3), (2009), 625-633.
  • F. G. Feyziyev, A. M. Babavand, Description of decoding of cyclic codes in the class of sequential machines based on the Meggitt theorem. Automatic Control and Computer Sciences 46, (2012), 164–169.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Muhammet Candan 0000-0002-3654-1816

Publication Date August 31, 2021
Published in Issue Year 2021 Volume: 10 Issue: 2

Cite

APA Candan, M. (2021). Optimal control processes associated with a class of stochastic sequential dynamical systems based on a parameter. Journal of New Results in Science, 10(2), 40-48.
AMA Candan M. Optimal control processes associated with a class of stochastic sequential dynamical systems based on a parameter. JNRS. August 2021;10(2):40-48.
Chicago Candan, Muhammet. “Optimal Control Processes Associated With a Class of Stochastic Sequential Dynamical Systems Based on a Parameter”. Journal of New Results in Science 10, no. 2 (August 2021): 40-48.
EndNote Candan M (August 1, 2021) Optimal control processes associated with a class of stochastic sequential dynamical systems based on a parameter. Journal of New Results in Science 10 2 40–48.
IEEE M. Candan, “Optimal control processes associated with a class of stochastic sequential dynamical systems based on a parameter”, JNRS, vol. 10, no. 2, pp. 40–48, 2021.
ISNAD Candan, Muhammet. “Optimal Control Processes Associated With a Class of Stochastic Sequential Dynamical Systems Based on a Parameter”. Journal of New Results in Science 10/2 (August 2021), 40-48.
JAMA Candan M. Optimal control processes associated with a class of stochastic sequential dynamical systems based on a parameter. JNRS. 2021;10:40–48.
MLA Candan, Muhammet. “Optimal Control Processes Associated With a Class of Stochastic Sequential Dynamical Systems Based on a Parameter”. Journal of New Results in Science, vol. 10, no. 2, 2021, pp. 40-48.
Vancouver Candan M. Optimal control processes associated with a class of stochastic sequential dynamical systems based on a parameter. JNRS. 2021;10(2):40-8.


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