Advertisement

Nonlinear Observer for Autonomous Switching Systems with Jumps

  • Mohamed Djemai
  • Noureddine Manamanni
  • Jean Pierre Barbot
Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 457)

Abstract

This work deals with nonlinear observer synthesis for a particular class of hybrid dynamic systems (HDS): autonomous switching systems with jumps. The jumps can result from the system’s dynamics or from the diffeomorphism, which makes it possible to lead the system to an observability canonical form. In this paper, our contribution relates to the design of a second order sliding mode based observer (“Super Twisting Algorithm”). It allows for estimating both continuous and discrete state related to the active dynamic. On the other hand, these observers ensure a finite time convergence of the estimation error.

References

  1. 1.
    Antsaklis, P.J. (ed.): Special issue on hybrid control systems. Proc. IEEE 43(4), pp. 452–587 (1998)Google Scholar
  2. 2.
    Branicky, M.S.: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Autom. Control 43(2), 461–474 (1998)Google Scholar
  3. 3.
    Saadaoui, H., Manamani, N., Djemai, M., Barbot, J.P., Floquet, T.: Exact differentiation and sliding mode observer for switched Lagrangian systems. In: Nonlinear Analysis: Theory, Methods & Applications, special issue: Hybrid Systems and Applications, pp. 1–20 (2005)Google Scholar
  4. 4.
    DeCarlo, R., Branicky, M., Pettersson, S., Lennartson, B.: Perspectives and results on the stability and stabilizability of hybrid systems. Proc. IEEE 88(7), 1069–1082 (2000)Google Scholar
  5. 5.
    Pettersson, S., Lennartson, B.: Hybrid system stability and robustness verification using linear matrix inequalities. Int. J. Control 75(16/17), 1335–1355 (2002)Google Scholar
  6. 6.
    Alessandri, A., Coletta, P.: Switching observers for continuous time and discrete-time linear systems. In: Proceedings of the American Control Conference, Arlington, Virginia, pp. 2516–2521 (2001)Google Scholar
  7. 7.
    Juloski, A. L., Heemels, W. P. M. H., Boers, Y., Verschure, F.: Two approaches to state estimation for a class of piecewise affine systems. In: Proceedings of the 42nd IEEE Conference on Decision and Control. Maui, Hawaii, USA. pp. 143–148 (2003)Google Scholar
  8. 8.
    Juloski, A.L., Heemels, W.P.M.H., Weiland, S.: Observer design for a class of piecewise affine systems. In: Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, USA, pp. 2606–2611 (2002)Google Scholar
  9. 9.
    Pettersson, S.: Observer design for switched systems using multiple quadratic Lyapunov functions. In: Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation 27–29 June 2005 pp. 262–267 (2005)Google Scholar
  10. 10.
    De la Sen, M., Luo, N.: Design of linear observers for a class of linear hybrid systems. Int. J. Syst. Sci. 31(9), 1077–1090 (2000)CrossRefMATHGoogle Scholar
  11. 11.
    Balluchi, A., Benvenutiz, L., Di Benedetto, M.D., Sangiovanni Vincentelliy, A.L.: A Hybrid Observer for the Driveline Dynamics. ECC-2001 (2001)Google Scholar
  12. 12.
    Lin, L., Linawati, Lie Josa, Ambikarajah, E.: A hybrid state estimation scheme for power systems. Asian Pacific Conf. 1, 555–558 (2002)Google Scholar
  13. 13.
    Boukhobza, T., Djemai, M., Barbot, J. P.: Nonlinear sliding observer for systems in output and output derivative injection form. In: Proceedings of the IFAC World Congres San Francisco (1996)Google Scholar
  14. 14.
    Lygeros, J., Johansson, H.K., Simć, S.N., Zhang, J., Sastry, S.S.: Dynamical properies of hybrid automata. EEE Trans. Autom. Control 48(1), 2–17 (2003)CrossRefGoogle Scholar
  15. 15.
    Hermann, R., Krener, A.J.: Nonlinear controllability and observability. IEEE Trans. Autom. Control, 22 9, 728–740 (1977)MathSciNetCrossRefGoogle Scholar
  16. 16.
    De Santis, E., Di Benedetto, M.D., Girasole, G.: Digital Idle Speed Control of Automative Engines using Hybrid Models. IFAC World Congress, Prague (2005)Google Scholar
  17. 17.
    Djemai, M., Manamani, N., Barbot, J.P.: Sliding mode observer for triangular input hybrid system. In: Proceedings of the IFAC World Congres Prague (2005)Google Scholar
  18. 18.
    Bemporad, A., Ferrari-Trecate, G., Morari, M.: Observability and controllability of piecewise affine and hybrid systems. IEEE Trans. Autom. Control 45(10), 1864–1876 (2000)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Boutat, D., Benali, A., Barbot, J.P.: About the observability of piecewise dynamical systems. NOLCOS-2004. (CD-ROM) (2004)Google Scholar
  20. 20.
    Fliess, M.: Generalized controller canonical forms for linear and nonlinear dynamics. IEEE Trans. Autom. Control, 35 9, 994–1000 (1990)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Levant, A.: Robust exact differentiation via sliding mode terchnique. In Autom. 34(3), 379–384 (1998)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Fridman L., Levant, A.: Sliding modes of higher order as a natural phenomenon in control theory. In: Garofalo, F., Glielmo, L. (eds.) Robust control via variable structure & Lyapunov techniques. Lecture Notes in control and Information Science 217. Springer, London, p. 107 (1996)Google Scholar
  23. 23.
    Petterson, S.: Sythesis of switched linear systems. In: Proceedings of the 42nd IEEE-CDC, Hawaii, USA (2003)Google Scholar
  24. 24.
    Raibert, M.: Legged Robot that Balance. MIT Press, Cambridge (1986)Google Scholar
  25. 25.
    Buhler, M., Koditschek, D.: From stable to chaotic juggling: theory, simulation and experiments. In: Proceeding of the IEEE Conference on Robotics and Automation (1990)Google Scholar
  26. 26.
    Scientific Software, Using simulink and stateflow in automative applications, Simulink-Stateflow Technical Examples. The MathWorks Inc. (1998)Google Scholar
  27. 27.
    Levant, A.: Higher order sliding modes and arbitrary-order exact robust differentiation. In: Proceedings of the European Control Conference (2001)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Mohamed Djemai
    • 1
  • Noureddine Manamanni
    • 2
  • Jean Pierre Barbot
    • 3
  1. 1.LAMIH, CNRS UMR 8201University of Valenciennes and Hainaut CambresisValenciennesFrance
  2. 2.CReSTIC EA3804Université de Reims Champagne ArdenneReimsFrance
  3. 3.ENSEACergy-PontoiseFrance

Personalised recommendations