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nonlinear system; time-delay system; observability
The problem of state reconstruction from input and output measurements for nonlinear time delay systems is studied in this paper and a state observer is proposed that is easy to implement and, under suitable assumptions on the system and on the input function, gives exponential observation error decay. The proposed observer is itself a delay system and can be classified as an identity observer, in that it is such that if at a given time instant the system and observer states coincide, on a suitable Hilbert space, the observation error remains zero in all following time instants. The computation of the observer gain is straightforward. Computer simulations are reported that show the good performance of the observer.
[1] Banks H. T., Kappel F.: Spline approximations for functional differential equations. J. Differential Equations 34 (1979), 496–522 DOI 10.1016/0022-0396(79)90033-0 | MR 0555324 | Zbl 0422.34074
[2] Bensoussan A., Prato G. Da, Delfour M. C., Mitter S. K.: Representation and control of Infinite Dimensional Systems. Birkhauser, Boston 1992 MR 2273323 | Zbl 1117.93002
[3] Ciccarella G., Mora, M. Dalla, Germani A.: A Luenberger-like observer for nonlinear systems. Internat. J. Control 57 (1993), 3, 537–556 DOI 10.1080/00207179308934406 | MR 1205006 | Zbl 0772.93018
[4] Mora M. Dalla, Germani, A., Manes C.: Design of state observers from a drift-observability property. IEEE Trans. Automat. Control 45 (2000), 6, 1536–1540 DOI 10.1109/9.871767 | MR 1797411
[5] Dambrine M., Goubet, A., Richard J. P.: New results on constrained stabilizing control of time-delay systems. In: Proc. 34th IEEE Conference on Decision and Control, Vol. 2, New Orleans 1995, pp. 2052–2057
[6] Fairman F. W., Kumar A.: Delayless observers for systems with delay. IEEE Trans. Automat.Control AC-31 (1986), 3, 258–259 DOI 10.1109/TAC.1986.1104228 | Zbl 0597.93010
[7] Fattouh A., Sename, O., Dion J. M.: Robust observer design for time-delay sysems: a Riccati equation approach. Kybernetika 35 (1999), 6, 753–764 MR 1747974
[8] Germani A., Manes, C., Pepe P.: Linearization of input-output mapping for nonlinear delay systems via static state feedback. In: Proc. of IMACS Multiconference on Computational Engineering in Systems Applications, Vol. 1, Lille 1996, pp. 599–602
[9] Germani A., Manes, C., Pepe P.: Linearization and Decoupling of nonlinear delay systems. In: Proc. IEEE 1998 American Control Conference (ACC’98), Philadelphia 1998
[10] Germani A., Manes, C., Pepe P.: A state observer for nonlinear delay systems. In: Proc. 37th IEEE Conference on Decision and Control (CDC’98), Tampa 1998, Vol. 1, pp. 355–360
[11] Germani A., Manes, C., Pepe P.: An observer for M. I.M.O. nonlinear delay systems. In: IFAC World Congress 99, Beijing 1999, Vol. E, pp. 243–248
[12] Germani A., Manes C.: State observers for nonlinear systems with Smooth/Bounded Input. Kybernetika 35 (1999), 4, 393-413 MR 1723526
[13] Germani A., Manes, C., Pepe P.: Local asymptotic stability for nonlinear state feedback delay systems. Kybernetika 36 (2000), 1, 31–42 MR 1760886
[14] Germani A., Manes, C., Pepe P.: State observation of nonlinear systems with delayed Output Measurements. In: IFAC Workshop on Time Delay Systems (LTDS2000), Ancona 2000
[15] Germani A., Manes, C., Pepe P.: A twofold spline approximation for finite horizon LQG control of hereditary systems. SIAM J. Control Optim. 39 (2000), 4, 1233–1295 DOI 10.1137/S0363012998337461 | MR 1814274 | Zbl 1020.93030
[16] Gibson J. S.: Linear quadratic optimal control of hereditary differential systems: infinite-dimensional Riccati equations and numerical approximations. SIAM J. Control Optim. 31 (1983), 95–139 DOI 10.1137/0321006 | MR 0688442 | Zbl 0557.49017
[17] Isidori A.: Nonlinear Control Systems. Third edition. Springer–Verlag, Berlin 1995 Zbl 0931.93005
[18] Lee E. B., Olbrot A. W.: Observability and related structural results for linear hereditary systems. Internat. J. Control 34 (1981), 6, 1061–1078 DOI 10.1080/00207178108922582 | MR 0643872 | Zbl 0531.93015
[19] Lehman B., Bentsman J., Lunel S. V., Verriest E. I.: Vibrational control of nonlinear time lag systems with bounded delay: averaging theory, stabilizability, and transient behavior. IEEE Trans. Automat. Control 5 (1994), 898–912, 1994 DOI 10.1109/9.284867 | MR 1274337 | Zbl 0813.93044
[20] Moog C. H., Castro, R., Velasco M.: The disturbance decoupling problem for nonlinear systems with multiple time-delays: static state feedback solutions. In: Proc. IMACS Multiconference on Computational Engineering in Systems Applications, Lille 1996
[21] Olbrot A. W.: Observability and observers for a class of Linear systems with delays. IEEE Trans. Automat. Control AC-26 (1981), 2, 513–517 DOI 10.1109/TAC.1981.1102616 | MR 0613565 | Zbl 0474.93019
[22] Pearson A. E., Fiagbedzi Y. A.: An observer for time lag systems. IEEE Trans. Automat. Control 34 (1989), 7, 775–777 DOI 10.1109/9.29412 | MR 1000675 | Zbl 0687.93011
[23] Rosen I. G.: Difference equation state approximations for nonlinear hereditary control problems. SIAM J. Control Optim. 2 (1984), 302–326 DOI 10.1137/0322021 | MR 0732430 | Zbl 0579.49026
[24] Salamon D.: Observers and duality between observation and state feedback for time delay systems. IEEE Trans. Automat. Control AC-25 (1980), 6, 1187–1192 DOI 10.1109/TAC.1980.1102507 | MR 0601503 | Zbl 0471.93011
[25] Watanabe K.: Finite spectrum assignment and observer for multivariable systems with commensurate delays. IEEE Trans. Automat. Control AC-31 (1986), 6, 543–550 DOI 10.1109/TAC.1986.1104336 | MR 0839083 | Zbl 0596.93009
[26] Yao Y. X., Zhang Y. M., Kovacevic R.: Functional observer and state feedback for input time-delay systems. Internat. J. Control 66 (1997), 4, 603–617 DOI 10.1080/002071797224612 | MR 1673792 | Zbl 0873.93015
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