Contents
The problem of observer design naturally arises in a system approach, as soon as one needs some internal information from external (directly available) measurements. In general indeed, it is clear that one cannot use as many sensors as signals of interest characterizing the system behavior (for cost reasons, technological constraints, etc.), especially since such signals can come in a quite large number, and they can be of various types: they typically include time-varying signals characterizing the system (state variables), constant ones (parameters), and unmeasured external ones (disturbances).
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Alamir, M.: Optimization-based nonlinear observers revisited. Int. Journal of Control 72(13), 1204–1217 (1999)
Arcak, M., Kokotović, P.: Nonlinear observers: a circle criterion design and robustness analysis. Automatica 37(12), 1923–1930 (2001)
Barbot, J.P., Boukhobza, T., Djemai, M.: Sliding mode observer for triangular input form. In: Proc. 35th IEEE Conf. on Decision and Control, Kobe, Japan, pp. 1489–1490. IEEE Computer Society Press, Los Alamitos (1996)
Besançon, G.: Further results on high gain observers for nonlinear systems. In: Proc. 38th IEEE Conf. on Decision and Control, Phoenix, USA, IEEE Computer Society Press, Los Alamitos (1999)
Besançon, G.: On output transformations for state linearization up to output injections of nonlinear systems. IEEE Trans. on Automatic Control 44(11), 1975–1981 (1999)
Besançon, G.: A viewpoint on observability and observer design for nonlinear systems. In: Nijmeijer, H., Fossen, T. (eds.) New Directions in Nonlinear Observer Design. Lecture Notes in Control and Information Science, vol. 244, pp. 2–21. Springer, London (1999)
Besançon, G.: Observer design for nonlinear systems. In: Loría, A., Lamnabhi-Lagarrigue, F., Panteley, E. (eds.) Advanced topics in control systems theory. Lecture Notes in Control and Information Science, vol. 328, pp. 61–89. Springer, London (2006)
Besançon, G., Bornard, G.: State equivalence based observer design for nonlinear control systems. In: Proc. of IFAC World Congress, San Francisco, CA, USA, pp. 287–292 (1996)
Besançon, G., Bornard, G.: On charactering classes of observer forms for nonlinear systems. In: Proc. 4th European Control Conf., Brussels, Belgium (1997)
Besançon, G., Bornard, G., Hammouri, H.: Observer synthesis for a class of nonlinear control systems. European J. of Control 3(1), 176–193 (1996)
Besançon, G., Ţiclea, A.: Immersion-based observer design for rank-observable nonlinear systems. IEEE Trans. on Automatic Control 52(1), 83–88 (2007)
Besançon, G., Hammouri, H.: On uniform observation of non-uniformly observable systems. Systems & Control Letters 33(1), 1–11 (1996)
Besançon, G., Hammouri, H.: On observer design for interconnected systems. Journal of Math. Systems, Estimation and Control 8(3) (1998)
Bestle, D., Zeitz, M.: Canonical form observer design for nonlinear time-variable systems. Int. Journal of Control 38(2), 419–431 (1983)
Bornard, G., Celle-Couenne, F., Gilles, G.: Observability and observers. In: Nonlinear Systems - T.1, Modeling and Estimation, pp. 173–216. Chapman & Hall, London (1995)
Bornard, G., Couenne, N., Celle, F.: Regularly persistent observer for bilinear systems. In: New Trends in Nonlinear Control Theory. Lecture Notes in Control and Information Science, vol. 122, pp. 130–140. Springer, Berlin (1988)
Bornard, G., Hammouri, H.: A high gain observer for a class of uniformly observable systems. In: Proc. 30th IEEE Conf. on Decision and Control, Brighton, England, Dec 1991, pp. 1494–1496. IEEE Computer Society Press, Los Alamitos (1991)
Bornard, G., Hammouri, H.: A graph approach to uniform observability of nonlinear multi output systems. In: 40th IEEE Conf. on Decision and Control, Las Vegas, USA, IEEE Computer Society Press, Los Alamitos (2002)
Conte, G., Moog, C., Perdon, A.: Nonlinear control systems: an algebraic setting. Springer, Berlin (1999)
Deza, F., Bossanne, D., Busvelle, E., Gauthier, J.P., Rakotopara, D.: Exponential observers for nonlinear systems. IEEE Trans. on Automatic Control 38(3), 482–484 (1993)
Drakunov, S., Utkin, V.: Sliding mode observers. tutorial. In: Proc. 34th IEEE Conf. on Decision and Control, New Orleans, LA, USA, pp. 3376–3378. IEEE Computer Society Press, Los Alamitos (1995)
Fliess, M., Kupka: A finiteness criterion for nonlinear input-output differential systems. Siam Journal on Control and Optimization 21(5), 721–728 (1983)
Gauthier, J.P., Bornard, G.: Observability for any u(t) of a class of nonlinear systems. IEEE Trans. on Automatic Control 26(4), 922–926 (1981)
Gauthier, J.P., Hammouri, H., Othman, S.: A simple observer for nonlinear systems - applications to bioreactors. IEEE Trans. on Automatic Control 37(6), 875–880 (1992)
Gauthier, J.P., Kupka, A.K.: Observability and observers for nonlinear systems. Siam Journal on Control and Optimization 32(4), 975–994 (1994)
Gauthier, J.P., Kupka, A.K.: Deterministic observation theory and applications. Cambridge University Press, Cambridge (1997)
Gelb, A.: Applied optimal estimation. MIT Press, Cambridge (1992)
Glumineau, A., Moog, C., Plestan, F.: New algebraic-geometric conditions for the linearization by input-output injection. IEEE Trans. on Automatic Control 41(4), 598–603 (1996)
Hammouri, H., Celle, F.: Some results about nonlinear systems equivalence for the observer synthesis. In: New Trends in Systems Theory, pp. 332–339. Birkhäuser, Basel (1991)
Hammouri, H., Gauthier, J.P.: Bilinearization up to output injection. Systems & Control Letters 11, 139–149 (1988)
Hammouri, H., Kinnaert, M.: A new formulation for time-varying linearization up to output injection. Systems & Control Letters 28, 151–157 (1996)
Hammouri, H., De Leon Morales, J.: Observer synthesis for state-affine systems. In: Proc. 29th IEEE Conf. on Decision and Control, Honolulu, HA, USA, pp. 784–785. IEEE Computer Society Press, Los Alamitos (1990)
Hermann, R., Krener, A.J.: Nonlinear controllability and observability. IEEE Trans. on Automatic Control 22(5), 728–740 (1977)
Isidori, A.: Nonlinear Control Systems, 3rd edn. Springer, Berlin (1995)
Jouan, P.: Immersion of nonlinear systems into linear systems modulo output injection. Siam Journal on Control and Optimization 41, 1756–1778 (2003)
Kalman, R.E., Bucy, R.S.: New results in linear filtering and prediction theory. J. Basic Eng. 83, 95–108 (1961)
Khalil, H.: Nonlinear Systems, 2nd edn. Prentice-Hall, Englewood Cliffs (1996)
Krener, A.J., Isidori, A.: Linearization by output injection and nonlinear observers. Systems & Control Letters 3, 47–52 (1983)
Krener, A.J., Respondek, W.: Nonlinear observers with linearizable error dynamics. Siam Journal on Control and Optimization 23(2), 197–216 (1985)
Kwakernaak, H., Sivan, R.: Linear Optimal Control Systems. Wiley-Interscience, New York (1972)
Lévine, J., Marino, R.: Nonlinear systems immersion, observers and finite dimensional filters. Systems & Control Letters 7, 137–142 (1986)
Luenberger, D.G.: Observers for multivariable systems. IEEE Trans. on Automatic Control 11(2), 190–197 (1966)
Michalska, H., Mayne, D.Q.: Moving horizon observers and observer-based control. IEEE Trans. on Automatic Control 40(6), 995–1006 (1995)
Moreno, J.: Observer design for nonlinear systems: a dissipative approach. In: IFAC Symp. Systems Structure and Control, Oaxaca, Mex (2004)
Rudolph, J., Zeitz, M.: A block triangular nonlinear observer normal form. Systems & Control Letters 23, 1–8 (1994)
Sussmann, H.J.: Single input observability of continuous time systems. Math. Systems Theory 12, 371–393 (1979)
Zimmer, G.: State observation by on-line minimization. Int. Journal of Control 60(4), 595–606 (1994)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Besançon, G. (2007). An Overview on Observer Tools for Nonlinear Systems. In: Nonlinear Observers and Applications. Lecture Notes in Control and Information Sciences, vol 363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73503-8_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-73503-8_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73502-1
Online ISBN: 978-3-540-73503-8
eBook Packages: EngineeringEngineering (R0)