Skip to main content
SpringerLink
Log in

Variable Structure Observers for Nonlinear Interconnected Systems

  • Chapter
  • First Online:
Advances in Variable Structure Systems and Sliding Mode Control—Theory and Applications

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 115))

Abstract

In this chapter, a variable structure observer is designed for a class of nonlinear large-scale interconnected systems in the presence of uncertainties and nonlinear interconnections. The modern geometric approach is used to explore system structure and a transformation is employed to facilitate the observer design. Based on the Lyapunov direct method, a set of conditions are developed such that the proposed variable structure systems can be used to estimate the states of the original interconnected systems asymptotically. The internal dynamical structure of the isolated nominal subsystems as well as the structure of the uncertainties are employed to reduce conservatism. The bounds on the uncertainties are nonlinear and are employed in the observer design to enhance robustness. A numerical example is presented to illustrate the results and simulation studies show that the proposed approach is effective.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Aldeen, M.: Class of stabilising decentralised controllers for interconnected dynamical systems. IEE Proc. D-Contr. Theory App. 139(2), 125–134 (1992)

    Article  MATH  Google Scholar 

  2. Aoki, M.: Control of large-scale dynamic systems by aggregation. IEEE Trans. Autom. Control 13(3), 246–253 (1968)

    Article  Google Scholar 

  3. Aoki, M., Li, M.: Partial reconstruction of state vectors in decentralized dynamic systems. IEEE Trans. Autom. Control 18(3), 289–292 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bakule, L.: Decentralized control: An overview. Ann. Rev. Contr. 32(1), 87–98 (2008)

    Article  MathSciNet  Google Scholar 

  5. Chen, B.M.: Robust and \(H_{\infty }\) control Series. Communication and control engineering. Springer, Berlin (2000)

    MATH  Google Scholar 

  6. Dashkovskiy, S., Naujok, L.: Quasi-ISS/ISDS observers for interconnected systems and applications. Syst. Control Lett. 77, 11–21 (2015)

    Google Scholar 

  7. Diao, Z.F., Yan, X.G.: Robust observer design for a class of nonlinear systems using the system internal dynamics structure. J. Optim. Theory Appl. 138(2), 175–187 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Edwards, C., Spurgeon, S.: Sliding Mode Control: Theory and Applications. CRC Press, USA (1998)

    MATH  Google Scholar 

  9. Edwards, C., Yan, X.G., Spurgeon, S.K.: On the solvability of the constrained Lyapunov problem. IEEE Trans. Autom. Control 52(10), 1982–1987 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. Galimidi, A., Barmish, B.: The constrained Lyapunov problem and its application to robust output feedback stabilization. IEEE Trans. Autom. Control 31(5), 410–419 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gavel, D.T., Siljak, D.D.: Decentralized adaptive control: structural conditions for stability. IEEE Trans. Autom. Control 34(4), 413–426 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ghadami, R. Shafai, B.: Decentralized PI observer-based control of nonlinear interconnected systems with disturbance attenuation. In: Proceedings of American Control Conference, San Francisco, CA, USA. IEEE, pp. 4705–4710 (2011)

    Google Scholar 

  13. Hassan, K.K.: Nonlinear Systems. Prentice Hall, USA (2002)

    MATH  Google Scholar 

  14. Hua, C., Li, Y., Wang, H., Guan, X.: Decentralised fault-tolerant finite-time control for a class of interconnected nonlinear systems. IET Contr. Theory App. 9(16), 2331–2339 (2015)

    Article  Google Scholar 

  15. Isidori, A.: Nonlinear Control Systems. Springer, Berlin (1995)

    Book  MATH  Google Scholar 

  16. Keliris, C., Polycarpou, M.M., Parisini, T.: A robust nonlinear observer-based approach for distributed fault detection of input-output interconnected systems. Autom. 53, 408–415 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  17. Krstic, M., Kanellakopoulos, I., Kokotovic, P.V.: Nonlinear and Adaptive Control Design. Wiley, New York (1995)

    MATH  Google Scholar 

  18. Li, F., Wu, L., Shi, P., Lim, C.C.: State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties. Autom. 51, 385–393 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  19. Lim, Y.H., Ahn, H.S.: Decentralized control of nonlinear interconnected systems under both amplitude and rate saturations. Autom. 49(8), 2551–2555 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  20. Luenberger, D.G.: Observing the state of a linear system. IEEE Trans. on Mil. Elect. 8(2), 74–80 (1964)

    Article  Google Scholar 

  21. Lunze, J.: Feedback Control of Large Scale Systems. Prentice Hall PTR, USA (1992)

    MATH  Google Scholar 

  22. Mahmoud, M.S.: Decentralized Systems with Design Constraints, pp. 129–151. Springer, Berlin (2011)

    Book  MATH  Google Scholar 

  23. Mahmoud, M.S.: Decentralized state-estimation of interconnected systems with unknown nonlinearities. J. Opt. Theory App. 152(3), 786–798 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  24. Modarres, A.A., Momeni, H., Yazdizadeh, A.: A new decentralized sliding mode observer design for interconnected power systems with unknown and time-varying delay. In: Proceeding of the 4th Conference on Thermal Power Plants, pp. 1–6 (2012)

    Google Scholar 

  25. Reppa, V., Polycarpou, M.M., Panayiotou, C.G.: Decentralized isolation of multiple sensor faults in large-scale interconnected nonlinear systems. IEEE Trans. Autom. Control 60(6), 1582–1596 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  26. Saksena, V., Cruz, J.: An approach to decentralized control of large scale systems using aggregation methods. IEEE Trans. Autom. Control 30(9), 912–914 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  27. Sandell, N., Varaiya, P., Athans, M., Safonov, M.: Survey of decentralized control methods for large scale systems. IEEE Trans. Autom. Control 23(2), 108–128 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  28. Sastry, S., Bodson, M.: Adaptive Control: Stability. Convergence and robustness. Prentic-Hall, New Jersey (1994)

    MATH  Google Scholar 

  29. Sharma, R., Aldeen, M.: Fault and disturbance reconstruction in non-linear systems using a network of interconnected sliding mode observers. IET Control Theory Appl. 5(6), 751–763 (2011)

    Article  MathSciNet  Google Scholar 

  30. Shtessel, Y., Edwards, C., Fridman, L., Levant, A.: Sliding Mode Control and Observation. Springer, New York (2014)

    Book  Google Scholar 

  31. Siljak, D., Vukcevic, M.: Decentralization, stabilization, and estimation of large-scale linear systems. IEEE Trans. Autom. Control 21(3), 363–366 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  32. Spurgeon, S.K.: Sliding mode observers: a survey. Int. J. Sys. Sci. 39(8), 751–764 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  33. Sundareshan, M.K. Decentralized observation in large-scale systems. In: Proceedings in Decision and Control including the 15th Symposium on Adaptive Processes, 1976 IEEE Conference, pp. 659–664 (1976)

    Google Scholar 

  34. Sundareshan, M.K., Elbanna, R.M.: Design of decentralized observation schemes for large-scale interconnected systems: Some new results. Autom. 26(4), 789–796 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  35. Swarnakar, A., Marquez, H.J., Chen, T.: A new scheme on robust observer based control design for nonlinear interconnected systems with application to an industrial utility boiler. In: Proceedings of the American Control Conference, IEEE, New York City, USA, pp. 5601-5606 (2007)

    Google Scholar 

  36. Vadim, I.U.: Survey paper variable structure systems with sliding modes. IEEE Trans. Autom. Control 22(2), 212–222 (1977)

    Article  MATH  Google Scholar 

  37. Utkin, V., Guldner, J., Shi, J.: Sliding Mode Control in Electro-Mechanical Systems. CRC press, USA (2009)

    Book  Google Scholar 

  38. Wang, Y., Fei, J.: Adaptive fuzzy sliding mode control for PMSM position regulation system. Int. J. Innov. Comput. Inf. Control. 11(3), 881–891 (2015)

    Google Scholar 

  39. Wu, H.: Decentralized adaptive robust state feedback for uncertain large-scale interconnected systems with time delays. J. Optim. Theory Appl. 126(2), 439–462 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  40. Wu, H.: Adaptive robust state observers for a class of uncertain nonlinear dynamical systems with delayed state perturbations. IEEE Trans. Autom. Control 54(6), 1407–1412 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  41. Xia, X.H., Gao, W.B.: Nonlinear observer design by observer error linearization. SIAM J. Control Optim. 27(1), 199–216 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  42. Yan, X.G., Lam, J., Xie, L.: Robust observer design for non-linear interconnected systems using structural characteristics. Int. J. Control 76(7), 741–746 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  43. Yan, X.G., Edwards, C.: Robust decentralized actuator fault detection and estimation for large-scale systems using a sliding mode observer. Int. J. Control 81(4), 591–606 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  44. Yan, X.G., Lam, J., Dai, G.: Decentralized robust control for nonlinear large-scale systems with similarity. Comput. Elect. Eng. 25(3), 169–179 (1999)

    Article  Google Scholar 

  45. Yan, X.G., Spurgeon, S.K., Edwards, C.: Decentralized output feedback sliding mode control of nonlinear large-scale systems with uncertainties. J. Optim. Theory Appl. 119(3), 597–614 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  46. Yan, X.G., Spurgeon, S.K., Edwards, C.: Decentralised stabilisation for nonlinear time delay interconnected systems using static output feedback. Autom. 49(2), 633–641 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  47. Yan, X.G., Spurgeon, S.K., Edwards, C.: State and parameter estimation for nonlinear delay systems using sliding mode techniques. IEEE Trans. Autom. Control 58(4), 1023–1029 (2013)

    Article  MathSciNet  Google Scholar 

  48. Yan, X.G., Spurgeon, S.K., Edwards, C.: Memoryless static output feedback sliding mode control for nonlinear systems with delayed disturbances. IEEE Trans. Autom. Control 59(7), 1906–1912 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  49. Yan, X.G., Spurgeon, S.K., Edwards, C.: Variable Structure Control of Complex Systems: Analysis and Design. Springer, Berlin (2017)

    Book  MATH  Google Scholar 

  50. Yang, G.H., Zhang, S.Y.: Decentralized control of a class of large-scale systems with symmetrically interconnected subsystems. IEEE Trans. Autom. Control 41(5), 710–713 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  51. Zeitz, M.: The extended Luenberger observer for nonlinear systems. Syst. Control Lett. 9(2), 149–156 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  52. Zhang, C., Li, H.: A generalized robust decentralized control methodology for a class of interconnected nonlinear systems subject to uncertainties and disturbances. Nonlinear Anal. Hybrid Syst. 22, 55–71 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  53. Zhao, G., Zhao, C., Cheng, J.: Decoupled Terminal Sliding-Mode Control for a Class of Under-Actuated Mechanical Systems With Hybrid Sliding Surfaces. Int. J. Innov. Comput Inf. Control. 10(6), 2011–2023 (2014)

    Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the support of the National Natural Science Foundation of China (61573180) for this work.

Author information

Authors and Affiliations

  1. School of Engineering and Digital Arts, University of Kent, Canterbury, CT2 7NT, UK

    Mokhtar Mohamed & Xing-Gang Yan

  2. Department of Electronic and Electrical Engineering, University College London, London, WC1E 7JE, UK

    Sarah K. Spurgeon

  3. College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, People’s Republic of China

    Zehui Mao

Authors
  1. Mokhtar Mohamed
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xing-Gang Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sarah K. Spurgeon
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zehui Mao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xing-Gang Yan .

Editor information

Editors and Affiliations

  1. School of Automation, Southeast University, Nanjing, China

    Shihua Li

  2. Research & Innovation Portfolio, RMIT University, Melbourne, Victoria, Australia

    Xinghuo Yu

  3. Division of Electrical Engineering, National Autonomous University of Mexico, Mexico City, Distrito Federal, Mexico

    Leonid Fridman

  4. Faculty of Science, Engineering and Technology, Swinburne University of Technology, Melbourne, Victoria, Australia

    Zhihong Man

  5. School of Automation, Southeast University, Nanjing, China

    Xiangyu Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Cite this chapter

Mohamed, M., Yan, XG., Spurgeon, S.K., Mao, Z. (2018). Variable Structure Observers for Nonlinear Interconnected Systems. In: Li, S., Yu, X., Fridman, L., Man, Z., Wang, X. (eds) Advances in Variable Structure Systems and Sliding Mode Control—Theory and Applications. Studies in Systems, Decision and Control, vol 115. Springer, Cham. https://doi.org/10.1007/978-3-319-62896-7_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-62896-7_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62895-0

  • Online ISBN: 978-3-319-62896-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation