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Synthesis of Fuzzy Terminal Controller for Chemical Reactor of Alcohol Production

  • Latafat A. GardashovaEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1095)

Abstract

The most investigated area in optimal control of discrete processes under uncertain conditions is optimal control of fuzzy systems, i.e. represented by different-type fuzzy equations. In this paper, the fuzzy terminal control problem described by a fuzzy relational equation (FRE) to take into account the fuzzy state and controls is discussed. Kernel of FRE-based method is Bellman-Zadeh approach. From this point of view, a fuzzy terminal control problem is transfigured to the multistage decision making scheme. The solution of the discussed problem is defined as intersection of fuzzy goal and fuzzy constraints. At the end, obtained fuzzy decisions were maximized.

Keywords

Fuzzy relation Fuzzy relational equation Optimal control Fuzzy condition Terminal regulator Reactor of alcohol production 

References

  1. 1.
    Aliev, R.A., Aliev, R.R.: Soft Computing and Its Application. World Scientific, New Jersey (2001)CrossRefGoogle Scholar
  2. 2.
    Aliev, R.A., Abdikiev, N.M., Shachnazarov, M.M.: Intelligent control systems, Moscow (1990). (in Russian)Google Scholar
  3. 3.
    Gardashova, L.A., Gahramanli, Y., Babanli, M..: Fuzzy neural network based analysis of the process of oil product sorption with foam polystyrene. Int. J. Eng. Res. Appl. 7(9), 85–90 (2017)Google Scholar
  4. 4.
    Di Nola, A., Pedrycz, W., Sessa, W.S.: Fuzzy relation equations and algorithms of inference mechanism in expert systems. In: Approximate Reasoning in Expert Systems, pp. 355–367. Elsevier Science Publishers B.V., North Holland, Amsterdam (1985)Google Scholar
  5. 5.
    Sanchez, E.: Resolution of composite fuzzy relation equations. Inf. Control 30, 38–48 (1976)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Martino, F.D., Sessa, S.: Spatial analysis and fuzzy relation equations. Adv. Fuzzy Syst. 2011, 1–14 (2011)Google Scholar
  7. 7.
    Li, Y.M., Wang, X.P.: Necessary and sufficient conditions for existence of maximal solutions for inf-α composite fuzzy relational equations. Comput. Math Appl. 55, 1961–1973 (2008)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Belohlavek, R.: Sup-t-norm and inf-residuum are one type of relational product: unifying framework and consequences. Fuzzy Sets Syst. 197, 45–58 (2012)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Xiong, Q.Q., Wang, X.P.: Solution sets of inf-αT fuzzy relational equations on complete Brouwerian lattices. Inf. Sci. 177, 4757–4767 (2007)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Markovski, A.V.: On the relation between equations with max-product composition and the covering problem. Fuzzy Sets Syst. 153, 261–273 (2005)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Lin, J.L.: On the relation between fuzzy max-Archimedean t-norm relational equations and the covering problem. Fuzzy Sets Syst. 160, 2328–2344 (2009)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Lin, J.L., Wu, Y.K., Guu, S.M.: On fuzzy relational equations and the covering problem. Inf. Sci. 181, 2951–2963 (2011)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Xiong, Q., Shu, Q.: Fuzzy relational equations and the covering problem. In: 16th World Congress of the International Fuzzy Systems Association (IFSA) and 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), pp. 77–84 (2015)Google Scholar
  14. 14.
    Zadeh, L.A.: Fuzzy sets. Inform. Control 8, 338–353 (1965)CrossRefGoogle Scholar
  15. 15.
    Bellman, R.E., Zadeh, L.A.: Decision making in a fuzzy environment. Manag. Sci. 17(4), 141–164 (1970)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Loia, V., Sessa, S.: Fuzzy relation equations for coding/decoding processes of images and videos. Inf. Sci. 171, 145–172 (2005)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Aliev, R.A., Pedrycz, W.: Fundamentals of a fuzzy-logic-based generalized theory of stability. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 39(4), 971–988 (2009)CrossRefGoogle Scholar
  18. 18.
    Aliev, R., Tserkovny, A.: Systemic approach to fuzzy logic formalization for approximate reasoning. Inf. Sci. 181(6), 1045–1059 (2011)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Azerbaijan State Oil and Industry UniversityBakuAzerbaijan

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