Optimal control processes associated with a class of stochastic sequential dynamical systems based on a parameter

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.

Keywords:

Optimal control process, Bellman’s equation, Dynamical programming Stochastic sequential dynamical systems,

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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.

ISSN: 1304-7981
Yayın Aralığı: Yılda 3 Sayı
Başlangıç: 2012
Yayıncı: Tokat Gaziosmanpaşa Üniversitesi

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