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Functional Observer-Based Sliding Mode Control for Discrete-Time Delayed Stochastic Systems

  • Satnesh SinghEmail author
  • S. Janardhanan
Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 483)

Abstract

This chapter addresses the problem of stabilisation, observer-based  sliding mode control, and functional observer-based  sliding mode control. An SMC method is proposed for discrete-time delayed stochastic systems. Stability and convergence analyses of the proposed method are provided. Furthermore, the DSMC of a delayed stochastic system for incomplete state information has also been considered, where states are estimated by the Kalman filter approach. A functional observer-based  SMC method for discrete-time delayed stochastic systems is proposed. Therefore, the SMC has been estimated by the functional observer approach. Finally, functional observer-based state feedback and the SMC law are compared graphically as well as numerically.

Keywords

Discrete-time systems Stochastic system State delay Sliding mode control State estimation Linear matrix inequalities Kalman filter Linear functional observer 

References

  1. 1.
    Kharitonov, V.: Time-Delay Systems: Lyapunov Functionals and Matrices. Control Engineering. Birkhäuser, Boston (2012)zbMATHGoogle Scholar
  2. 2.
    Cheres, E., Gutman, S., Palmor, Z.J.: IEEE Trans. Autom. Control 34(11), 1199 (1989).  https://doi.org/10.1109/9.40753CrossRefGoogle Scholar
  3. 3.
    Choi, H.H.: Electron. Lett. 30(13), 1100 (1994).  https://doi.org/10.1049/el:19940732CrossRefGoogle Scholar
  4. 4.
    Liao, X., Wang, L., Yu, P.: Stability of Dynamical Systems. Monograph Series on Nonlinear Science and Complexity. Elsevier Science, New York (2007)CrossRefGoogle Scholar
  5. 5.
    Xu, S., Lam, J., Yang, C.: Syst. Control Lett. 43(2), 77 (2001)CrossRefGoogle Scholar
  6. 6.
    Gouaisbaut, F., Dambrine, M., Richard, J.: Syst. Control Lett. 46(4), 219 (2002)CrossRefGoogle Scholar
  7. 7.
    Shi, P., Boukas, E.K., Shi, Y., Agarwal, R.K.: J. Comput. Appl. Math. 157(2), 435 (2003)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Song, H., Chen, S.C., Yam, Y.: IEEE Trans. Cybern. PP(99), 1 (2017).  https://doi.org/10.1109/TCYB.2016.2577340CrossRefGoogle Scholar
  9. 9.
    Hu, J., Wang, Z., Niu, Y., Gao, H.: J. Frankl. Inst. 351(4), 2185 (2014). Special Issue on 2010-2012 Advances in Variable Structure Systems and Sliding Mode AlgorithmsGoogle Scholar
  10. 10.
    Hu, J., Wang, Z., Gao, H., Stergioulas, L.K.: J. Frankl. Inst. 349(4), 1459 (2012). Special Issue on Optimal Sliding Mode Algorithms for Dynamic SystemsGoogle Scholar
  11. 11.
    Singh, S., Janardhanan, S.: In: 2015 International Workshop on Recent Advances in Sliding Modes (RASM), pp. 1–6 (2015)Google Scholar
  12. 12.
    Mehta, A.J., Bandyopadhyay, B.: ASME, J. Dyn. Syst. Meas. Contro 138, 124503 (2016)Google Scholar
  13. 13.
    Hu, J., Wang, Z., Gao, H., Stergioulas, L.K.: IEEE Trans. Ind. Electron. 59(7), 3008 (2012).  https://doi.org/10.1109/TIE.2011.2168791CrossRefGoogle Scholar
  14. 14.
    Kalman, R.E., Bucy, R.S.: Trans. ASME. Ser. D. J. Basic Eng. 109 (1961)Google Scholar
  15. 15.
    Rhodes, I.: IEEE Trans. Autom. Control 16(6), 688 (1971)CrossRefGoogle Scholar
  16. 16.
    Rao, B., Mahalanabis, A.: IEEE Trans. Autom. Control 16(3), 267 (1971)CrossRefGoogle Scholar
  17. 17.
    Liang, D., Christensen, G.: IEEE Trans. Autom. Control 20(1), 176 (1975).  https://doi.org/10.1109/TAC.1975.1100879CrossRefGoogle Scholar
  18. 18.
    Chen, B., Yu, L., Zhang, W.A.: IET Control Theory Appl. 5(17), 1945 (2011)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Trinh, H.: Int. J. Control 72(18), 1642 (1999)CrossRefGoogle Scholar
  20. 20.
    Darouach, M.: IEEE Trans. Autom. Control 46(3), 491 (2001)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Darouach, M.: IEEE Trans. Autom. Control 50(2), 228 (2005)CrossRefGoogle Scholar
  22. 22.
    Singh, S., Janardhanan, S.: Int. J. Syst. Sci. 48(15), 3246 (2017)CrossRefGoogle Scholar
  23. 23.
    Trinh, H., Huong, D.C., Hien, L.V., Nahavandi, S.: IEEE Trans. Circuits Syst. II: Express Briefs 64(5), 555 (2017)CrossRefGoogle Scholar
  24. 24.
    Nguyen, M.C., Trinh, H., Nam, P.T.: Int. J. Syst. Sci. 47(13), 3193 (2016)CrossRefGoogle Scholar
  25. 25.
    Islam, S.I., Lim, C.C., Shi, P.: J. Frankl. Inst. (2018)Google Scholar
  26. 26.
    Trinh, H., Huong, D.: J. Frankl. Inst. 355(3), 1411 (2018)CrossRefGoogle Scholar
  27. 27.
    Bandyopadhyay, B., Janardhanan, S.: Discrete-time Sliding Mode Control: A Multirate Output Feedback Approach. Lecture Notes in Control and Information Sciences. Springer, Berlin (2005)zbMATHGoogle Scholar
  28. 28.
    Koshkouei, A.J., Zinober, A.S.I.: ASME 122(4), 793 (2000).  https://doi.org/10.1115/1.1321266CrossRefGoogle Scholar
  29. 29.
    Xia, Y., Jia, Y.: IEEE Trans. Autom. Control 48(6), 1086 (2003)CrossRefGoogle Scholar
  30. 30.
    Xia, Y., Fu, M., Shi, P., Wang, M.: IET Control Theory Appl. 4(4), 613 (2010)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Xia, Y., Liu, G.P., Shi, P., Chen, J., Rees, D.: Int. J. Robust Nonlinear Control 18(11), 1142 (2008)CrossRefGoogle Scholar
  32. 32.
    Scherer, C., Weiland, S.: The Control Systems Handbook. Linear Matrix Inequalities in Control, 2nd edn. (2010)Google Scholar
  33. 33.
    Gahinet, P.: LMI Control Toolbox: For Use with MATLAB ; User’s Guide ; Version 1. Computation, visualization, programming (MathWorks) (1995)Google Scholar
  34. 34.
    Brewer, J.: IEEE Trans. Circuits Syst. 25(9), 772 (1978)CrossRefGoogle Scholar
  35. 35.
    Sage, A., Melsa, J.: Estimation Theory with Applications to Communications and Control. McGraw-Hill Series in Systems Science. McGraw-Hill, New York (1971)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Electrical EngineeringIndian Institute of Technology DelhiNew DelhiIndia

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