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Reduced-order dynamic observer error linearisation for discrete-time systems: an extension of the classical observer error linearisation

Reduced-order dynamic observer error linearisation for discrete-time systems: an extension of the classical observer error linearisation

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This study addresses reduced-order dynamic observer error linearisation (RDOEL) for discrete-time systems, which is a modified version of dynamic observer error linearisation (DOEL). The authors define the concept of RDOEL and provide a necessary and sufficient condition for RDOEL. Moreover, the relation between RDOEL and DOEL is discussed when the auxiliary dynamics is an arbitrary linear controllable system. Using the relationship and an existing algorithm for DOEL, an algorithm for RDOEL also proposed, which offers lower-dimensional observers than DOEL. Finally, the authors illustrate the theory by applying it to the discrete-time hyperchaotic system due to Wang, which was derived from the generalised Rössler system via a first-order difference algorithm.

References

    1. 1)
      • 1. Krener, J.A., Isidori, A.: ‘Linearization by output injection and nonlinear observers’, Syst. Control Lett., 1983, 3, (1), pp. 4752 (doi: 10.1016/0167-6911(83)90037-3).
    2. 2)
      • 2. Bestle, D., Zeitz, M.: ‘Canonical form observer design for non-linear time-variable systems’, Int. J. Control, 1983, 38, (2), pp. 419431 (doi: 10.1080/00207178308933084).
    3. 3)
      • 3. Krener, J.A., Respondek, W.: ‘Nonlinear observers with linearizable error dynamics’, SIAM J. Control Optim., 1985, 23, (2), pp. 197216 (doi: 10.1137/0323016).
    4. 4)
      • 4. Levine, J., Marino, R.: ‘Nonlinear system immersion, observers and finite-dimensional filters’, Syst. Control Lett., 1986, 7, (2), pp. 133142 (doi: 10.1016/0167-6911(86)90019-8).
    5. 5)
      • 5. Xia, H.X., Gao, W.B.: ‘Nonlinear observer design by observer error linearization’, SIAM J. Control Optim., 1989, 27, (1), pp. 199216 (doi: 10.1137/0327011).
    6. 6)
      • 6. Noh, D., Jo, N.H., Seo, J.H.: ‘Nonlinear observer design by dynamic observer error linearization’, IEEE Trans. Autom. Control, 2004, 49, (10), pp. 17461750 (doi: 10.1109/TAC.2004.835397).
    7. 7)
      • 7. Boutat, D., Benali, A., Hammouri, H., Busawon, K.: ‘New algorithm for observer error linearization with a diffeomorphism on the outputs’, Automatica, 2009, 45, (10), pp. 21872193 (doi: 10.1016/j.automatica.2009.05.030).
    8. 8)
      • 8. Wang, Y., Lynch, A.F.: ‘Multiple time scalings of a multiple-output observer form’, IEEE Trans. Autom. Control, 2010, 55, (4), pp. 966971 (doi: 10.1109/TAC.2010.2041616).
    9. 9)
      • 9. Leon, E.A., Solsona, J.A.: ‘Design of reduced-order nonlinear observers for energy conversion applications’, IET Control Theory Applic., 2010, 4, (5), pp. 724734 (doi: 10.1049/iet-cta.2009.0095).
    10. 10)
      • 10. Glumineau, A., Moog, C.H., Diop, S., Plestan, F.: ‘New algebro-geometric conditions for the linearization by input-output injection’, IEEE Trans. Autom. Control, 1996, 41, (4), pp. 598603 (doi: 10.1109/9.489283).
    11. 11)
      • 11. Guay, M., ‘Observer linearization by output-dependent time-scale transformation’, IEEE Trans. Autom. Control, 2002, 47, (10), pp. 17301735 (doi: 10.1109/TAC.2002.803547).
    12. 12)
      • 12. Respondek, W., Pogromsky, A., Nijmeijer, H.: ‘Time scaling for observer design with linearizable error dynamics’, Automatica, 2004, 40, (2), pp. 277285 (doi: 10.1016/j.automatica.2003.09.012).
    13. 13)
      • 13. Zheng, G., Boutat, D., Barbot, J.P.: ‘Single output-dependent observability normal form’, SIAM J. Control Optim., 2007, 46, (6), pp. 22422255 (doi: 10.1137/050627137).
    14. 14)
      • 14. Keller, H., ‘Non-linear observer design by transformation into a generalized observer canonical form’, Int. J. Control, 1987, 46, (6), pp. 19151930 (doi: 10.1080/00207178708934024).
    15. 15)
      • 15. Marino, R., Tomei, P.: ‘Adaptive observers with arbitrary exponential rate of convergence for nonlinear systems’, IEEE Trans. Autom. Control, 1995, 40, (7), pp. 13001304 (doi: 10.1109/9.400471).
    16. 16)
      • 16. C.Li, W., Tao, L.W.: ‘Observing non-linear time-variable systems through a canonical form observer’, Int. J. Control, 1986, 44, (6), pp. 17031713 (doi: 10.1080/00207178608933695).
    17. 17)
      • 17. Zheng, G., Boutat, D.: ‘Synchronisation of chaotic systems via reduced observers’, IET Control Theory Applic., 2011, 5, (2), pp. 308314 (doi: 10.1049/iet-cta.2010.0078).
    18. 18)
      • 18. Phelps, R.A., Krener, A.J.: ‘Computation of observer normal form using Macsyma’, in Byrnes, C.I., Martin, C.F., Saeks, R.E.: (Eds.): ‘Analysis and control of nonlinear systems’ (North-Holland, 1988), pp. 475482.
    19. 19)
      • 19. Röbenack, K., Lynch, A.F.: ‘An efficient method for observer design with approximately linear error dynamics’, Int. J. Control, 2004, 77, (7), pp. 607612 (doi: 10.1080/00207170410001682515).
    20. 20)
      • 20. Jouan, P.: ‘Immersion of nonlinear systems into linear systems modulo output injection’, SIAM J. Control Optim., 2003, 41, (6), pp. 17561778 (doi: 10.1137/S0363012901391706).
    21. 21)
      • 21. Back, J., Seo, J.H.: ‘Immersion of non-linear systems into linear systems up to output injection: characteristic equation approach’, Int. J. Control, 2004, 77, (8), pp. 723734 (doi: 10.1080/00207170410001715040).
    22. 22)
      • 22. Back, J., Seo, J.H.: ‘An algorithm for system immersion into nonlinear observer form: SISO case’, Automatica, 2006, 42, (2), pp. 321328 (doi: 10.1016/j.automatica.2005.09.014).
    23. 23)
      • 23. Back, J., Yu, K.T., Seo, J.H.: ‘Dynamic observer error linearization’, Automatica, 2006, 42, (12), pp. 21952200 (doi: 10.1016/j.automatica.2006.07.009).
    24. 24)
      • 24. Yu, K.T., Back, J., Seo, J.H.: ‘Constructive algorithm for dynamic observer error linearization via integrators: single output case’, Int. J. Robust Nonlinear Control, 2007, 17, (1), pp. 2549 (doi: 10.1002/rnc.1117).
    25. 25)
      • 25. Boutat, D., Busawon, K.: ‘On the transformation of nonlinear dynamical systems into the extended nonlinear observable canonical form’, Int. J. Control, 2011, 84, (1), pp. 94106 (doi: 10.1080/00207179.2010.541285).
    26. 26)
      • 26. Yang, J., Back, J., Seo, J.H., Shim, H.: ‘Reduced-order dynamic observer error linearization’. IFAC Symp. NOLCOS, Bologna, Italy, 2010.
    27. 27)
      • 27. Yang, J., Back, J., Seo, J.H.: ‘A complete solution to a simple case of dynamic observer error linearization: new approach to observer error linearization’. IEICE Trans. Fundamentals, 2011, E94-A, (1), pp. 424429 (doi: 10.1587/transfun.E94.A.424).
    28. 28)
      • 28. Yang, J.: ‘Nonlinear observer design by reduced-order dynamic observer error linearization’. PhD dissertation, Seoul National University, 2011.
    29. 29)
      • 29. Chung, S.-T., Grizzle, J.W.: ‘Sampled-data observer error linearization’, Automatica, 1990, 26, (6), pp. 9971007 (doi: 10.1016/0005-1098(90)90084-U).
    30. 30)
      • 30. Lee, W., Nam, K.: ‘Observer design for autonomous discrete-time nonlinear systems’, Syst. Control Lett., 1991, 17, pp. 4958 (doi: 10.1016/0167-6911(91)90098-Y).
    31. 31)
      • 31. Lin, W., Byrnes, C.I.: ‘Remarks on linearization of discrete-time autonomous systems and nonlinear observer design’, Syst. Control Lett., 1995, 25, pp. 3140 (doi: 10.1016/0167-6911(94)00054-Y).
    32. 32)
      • 32. Lilge, T.: ‘On observer design for nonlinear discrete-time systems’, Eur. J. Control, 1998, 4, pp. 306319 (doi: 10.1016/S0947-3580(98)70124-4).
    33. 33)
      • 33. Huijberts, H.J.C.: ‘On existence of extended observers for nonlinear discrete-time systems’, in Nijmeijer, H., Fossen, T.I. (Eds.): ‘New directions in nonlinear observer design’ (Springer-Verlag, London, 1999), pp. 7392.
    34. 34)
      • 34. Boutat, D., Boutat-Baddas, L., Darouach, M.: ‘A new reduced-order observer normal form for nonlinear discrete time systems’, Syst. Control Lett., 2012, 61, pp. 10031008 (doi: 10.1016/j.sysconle.2012.07.007).
    35. 35)
      • 35. Kazantzis, N., Kravaris, C.: ‘Discrete-time nonlinear observer design using functional equations’, Syst. Control Lett., 2001, 42, pp. 8194 (doi: 10.1016/S0167-6911(00)00071-2).
    36. 36)
      • 36. Xiao, M., Kazantzis, N., Kravaris, C., Krener, A.J.: ‘Nonlinear discrete-time observer design with linearizable error dynamics’, IEEE Trans. Autom. Control, 2003, 48, (4), pp. 622626 (doi: 10.1109/TAC.2003.809793).
    37. 37)
      • 37. Lin, W., Wei, J.: ‘Observer design for a class of discrete-time nonlinear systems’, Eur. J. Control, 2009, 15, pp. 184193 (doi: 10.3166/ejc.15.184-193).
    38. 38)
      • 38. Zhang, J., Feng, G., Xu, H.: ‘Observer design for nonlinear discrete-time systems: immersion and dynamic observer error linearization techniques’, Int. J. Robust Nonlinear Control, 2010, 20, (5), pp. 504514.
    39. 39)
      • 39. Wang, X.Y.: ‘Chaos in complex nonlinear systems’ (Publishing House of Electronics Industry, Beijing, 2003) (in Chinese).
    40. 40)
      • 40. Yan, Z.: ‘Q-S (complete or anticipated) synchronization backsteeping scheme in a class of discrete-time chaotic (hyperchaotic) systems: a symbolic-numeric computation approach’, Chaos, 2006, 16, (1), p. 013119 (doi: 10.1063/1.1930727).
    41. 41)
      • 41. Ding, Z.: ‘Differential stability and design of reduced-order observers for non-linear systems’, IET Control Theory Applic., 2011, 5, (2), pp. 315322 (doi: 10.1049/iet-cta.2009.0523).
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