Abstract
This paper deals with the problem of transforming a single output nonlinear system with an auxiliary dynamics into an extended nonlinear observer canonical form (ENOCF). The proposed ENOCF depends on system output and auxiliary state, and admits a kind of high-gain observer. We provide two necessary conditions and an equivalent condition for the existence of such a transformation, and then apply the results to the Rössler system as a case study.
Similar content being viewed by others
References
J. Lu, C. Feng, S. Xu, and Y. Chu, “Observer design for a class of uncertain state-delayed nonlinear systems,” Int. J. of Control, Automation, and Systems, vol. 4, no. 4, pp. 448–452, 2006.
M. M. Aly, H. A. A. Fatah, and A. Bahgat, “Nonlinear observers for spacecraft attitude estimation in case of yaw angle measurement absence,” Int. J. of Control, Automation, and Systems, vol. 8, no. 5, pp. 1018–1028, 2010.
M. Sharma and A. Verma, “Wavelet reduced order observer based adaptive tracking control for a class of uncertain nonlinear systems using reinforcement learning,” Int. J. of Control, Automation, and Systems, vol. 11, no. 3, pp. 496–502, 2013.
A. J. Krener and A. Isidori, “Linearization by output injection and nonlinear observers,” Syst. Control Lett., vol. 3, no. 1, pp. 47–52, 1983.
D. Bestle and M. Zeitz, “Canonical form observer design for non-linear time-variable systems,” Int. J. Control, vol. 38, no. 2, pp. 419–431, 1983.
A. J. Krener and W. Respondek, “Nonlinear observers with linearizable error dynamics,” SIMA J. Control Optim., vol. 23, no. 2, pp. 197–216, 1985.
M. Guay, “Observer linearization by outputdependent time-scale transformation,” IEEE Trans. Autom. Control, vol. 47, no. 10, pp. 1730–1735, 2002.
G. Zheng, D. Boutat, and J. Barbot, “Single output-dependent observability normal form,” SIAM J. Control Optim., vol. 46, no. 6, pp. 2242–2255, 2007.
P. Jouan, “Immersion of nonlinear systems into linear systems modulo output injection,” SIAM J. Control Optim., vol. 41, no. 6, pp. 1756–1778, 2003.
J. Back and J. H. Seo, “Immersion of non-linear systems into linear systems up to output injection: characteristic equation approach,” Int. J. Control, vol. 77, no. 8, pp. 723–734, 2004.
D. Noh, N. H. Jo, and J. H. Seo, “Nonlinear observer design by dynamic observer error linearization,” IEEE Trans. Autom. Control, vol. 49, no. 10, pp. 1746–1750, 2004.
J. Back, K. T. Yu, and J. H. Seo, “Dynamic observer error linearization,” Automatica, vol. 42, no. 12, pp. 2195–2200, 2006.
K. T. Yu, J. Back, and J. H. Seo, “Constructive algorithm for dynamic observer error linearization via integrators: single output case,” Int. J. Robust Nonlin. Control, vol. 17, no. 1, pp. 25–49, 2007.
J. Yang, J. Back, J. H. Seo, and H. Shim, “Re duced-order dynamic observer error linearization,” Proc. of IFAC Symp. NOLCOS, Bologna, Italy, 2010.
D. Boutat and K. Busawon, “On the transformation of nonlinear dynamical systems into the extended nonlinear observable canonical form,” Int. J. Control, vol. 84, no. 1, pp. 94–106, 2011.
J. Yang, J. Back, and J. H. Seo, “A complete solution to a simple case of dynamic observer error linearization: new approach to observer error linearization,” IEICE Trans. Fundamentals, vol. E94-A, no. 1, pp. 424–429, 2011.
R. Tami, D. Boutat, and G. Zheng, “Extended output depending normal form,” Automatica, vol. 49, no. 7, pp. 2192–2198, 2013.
K. Busawon, M. Farza, and H. Hammouri, “A simple observer for a class of nonlinear systems,” Applied Mathematics Letters, vol. 11, no. 3, pp. 27–31, 1998.
H. Nijmeijer and A. J. van der Schaft, Nonlinear Dynamical Control Systems, Springer-Verlag, New York, 1990.
N. H. Jo and J. H. Seo, “Observer design for nonlinear systems that are not uniformly observable,” Int. J. Control, vol. 75, no. 5, pp. 369–380, 2002.
O. E. Rössler, “An equation for hyperchaos,” Phys. Lett. A, vol. 71A, pp. 155–160, 1979.
Author information
Authors and Affiliations
Corresponding author
Additional information
Hansung Cho received his B.S. degree in Mathematics from Seoul National University, Korea, in 2005. He received his Ph.D. degree (the integrated M.S./Ph.D. course) in Electrical Engineering from Seoul National University, Korea in 2014. His research interests include analysis and control of nonlinear systems and hybrid systems.
Jongwook Yang received his B.S., M.S., and Ph.D. degrees in Electrical Engineering from Seoul Nation University, Korea, in 1999, 2001, and 2011, respectively. From 2012 to 2013, he had a position as a post-doctoral researcher at Seoul National University. His research interests include control system theory, robotics, and multi-agent systems.
Jin Heon Seo received his B.S. and M.S. degrees in Electrical Engineering from Seoul National University, Korea, in 1978 and 1980, and his Ph.D. degree in Electrical Engineering from University of California, Los Angeles, in 1985. He served as an Assistant Professor from 1985 to 1989 in the Department of Electrical Engineering at Texas Tech University, Lubbock. Since 1989, he has been with the School of Electrical Engineering at Seoul National University, Seoul, Korea, where he is currently a professor. His research interests include nonlinear systems theory, large scale systems control, and infinite dimensional system theory.
Rights and permissions
About this article
Cite this article
Cho, H., Yang, J. & Seo, J.H. Extended nonlinear observer canonical form depending on system output and auxiliary state. Int. J. Control Autom. Syst. 13, 25–32 (2015). https://doi.org/10.1007/s12555-013-0479-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-013-0479-9