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2013 | 42 | nr 2 | 505--525
Tytuł artykułu

On the Fuzzy Control Stochastic Differential Systems

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, fuzzy control stochastic differential systems are introduced. The existence and some comparison results on solutions of fuzzy control stochastic differential systems and on sheaf-solutions of sheaf fuzzy control stochastic systems are provided. The continuous dependence of solutions and sheaf-solutions on initials and controls is investigated. The results obtained are correct and meaningful for the theory control. (original abstract)
Słowa kluczowe
Rocznik
Tom
42
Numer
Strony
505--525
Opis fizyczny
Twórcy
  • Tay Nguyen University, Vietnam
Bibliografia
  • Diamond, P. and Kloeden, P. (1994) Metric Spaces of Fuzzy Sets. World Scientific, Singapore.
  • Fei, W. Y. (2007) Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients. Information Sciences 177, 4329-4337.
  • Fei, W. Y. (2013) Existence and uniqueness for solution to fuzzy stochastic differential equations driven by local martingales under the non-Lipschitzian conditions. Nonlinear Analysis TMA 76, 202-214.
  • Feng, Y. H. (1999A) Mean square integral and differential of fuzzy stochastic processes. Fuzzy Sets and Systems 102, 271-280.
  • Feng, Y. H. (1999b) Convergence theorems for fuzzy random variables and fuzzy martingales. Fuzzy Sets and Systems 103, 435-441.
  • Feng, Y. H. (2000a) Mean-square Riemann-Stieltjes integrals of fuzzy stochastic processes and their applications. Fuzzy Sets and Systems 110, 27-41.
  • Feng, Y. H. (2000b) Fuzzy stochastic differential systems. Fuzzy Sets and Systems 115, 351-363.
  • Feng, Y. H. (2001) Sum of independent fuzzy random variables. Fuzzy Sets and Systems 123, 11-18.
  • Feng, Y. H. (2003) The solutions of linear fuzzy stochastic differential systems. Fuzzy Sets and Systems 140, 541-554.
  • Kim, J. H. (2005) On fuzzy stochastic differential equations. Journal of Korean Mathematical Society 42 (1), 153-169.
  • Lakshmikantham, V. (2000) Uncertain systems and fuzzy differential equations. Journal Mathematical Analysis and Applications 251, 805-817.
  • Lakshmikantham, V. (2005) Set Differential Equations Versus Fuzzy Differential Equations. Applied Mathematics and Computation 164, 277-294.
  • Lakshmikantham, V., Bhaskar, T. G. and Devi, J. V. (2006) Theory of Set Differential Equations in Metric Spaces. Cambridge Scientific Publishers, UK.
  • Lakshmikantham, V. and Leela, S. (1969) Differential and Integral Inequalities, Vol. I. Academic Press, New York.
  • Lakshmikantham, V. and Mohapatra, R. (2003) Theory of Fuzzy Differential Equations and Inclusions. Taylor and Francis, London.
  • Malinowski, M. T. and Michta, M. (2011) Stochastic fuzzy differentia equations with an application. Kybernetika 47, 123-143.
  • Malinowski, M. T. and Michta, M. (2010) Fuzzy stochastic integral equations. Dynamic Systems and Applications 19, 473-494.
  • Michta, M. (2011) On set-valued stochastic integrals and fuzzy stochastic equations. Fuzzy Sets and Systems 177, 1-19.
  • Ovsanikov, D. A. (1980) Mathematical Methods for Sheaf-Control. Publisher of Leningrad University, Leningrad.
  • Phu, N. D., Quang, L. T. and Tung, T. T. (2008) Stability criteria for set control differential equations. Nonlinear Analysis TMA 69, 3715-3721.
  • Phu, N. D. and Tung, T. T. (2005) Sheaf-optimal control problem in fuzzy type. Journal of Science and Technology Development 8 (12), 5-11.
  • Phu, N. D. and Tung, T. T. (2006a) The comparison of sheaf-solutions in fuzzy control problems. Journal of Science and Technology Development 9 (2), 5-10.
  • Phu, N. D. and Tung, T. T. (2006b) Some properties of sheaf-solutions of sheaf fuzzy control problems. Electronic Journal of Differential Equations 108, 1-8.
  • Phu, N. D. and Tung, T. T. (2007) Some results on sheaf-solutions of sheaf set control problems. Nonlinear Analysis TMA 67, 1309-1315.
  • Puri, M.L. and Ralescu, D.A. (1986) Fuzzy random variables. Journal Mathematical Analysis and Applications 114, 409-422.
  • Tolstonogov, A. (2000) Differential Inclusions in a Banach Space. Kluwer Academic Publishers, Dordrecht.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171308235

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