Abstract
A methodology for the design of dynamical observers for hybrid plants is proposed. The hybrid observer consists of two parts: a location observer and a continuous observer. The former identifies the current location of the hybrid plant, while the latter produces an estimate of the evolution of the continuous state of the hybrid plant. A synthesis procedure is offered when a set of properties on the hybrid plant is satisfied. The synthesized hybrid observer identifies the current location of the plant after a finite number of steps and converges exponentially to the continuous state.
The work has been conducted with partial support of PARADES, a Cadence, Magneti-Marelli and ST-microelectronics E.E.I.G, by the European Community Projects IST-2001-33520 CC (Control and Computation) and IST-2001-32460 HYBRIDGE, and by CNR PF-MADESSII SP3.1.2.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. A. Ackerson and K. S. Fu. On state estimation in switching environments. IEEE Trans. on Automatic Control, 15(1):10–17, 1970.
A. Alessandri and P. Coletta. Design of luenberger observers for a class of hybrid linear systems. In Hybrid Systems: Computation and Control, volume 2034 of LNCS, pages 7–18. Springer-Verlag, Berlin Heidelberg, 2001.
A. Balluchi, L. Benvenuti, M. D. Di Benedetto, C. Pinello, and A. L. Sangiovanni-Vincentelli. Automotive engine control and hybrid systems: Challenges and opportunities. Proceedings of the IEEE, 88, “Special Issue on Hybrid Systems” (invited paper)(7):888–912, July 2000.
A. Balluchi, L. Benvenuti, M. D. Di Benedetto, and A. L. Sangiovanni Vincentelli. A hybrid observer for the driveline dynamics. In Proc. of the European Control Conference 2001, pages 618–623, Porto, P, 2001.
M. Branicky. Multiple lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. on Aut. Contr., 43(4):475–482, 1998.
P. E. Caines, R. Greiner, and S. Wang. Dynamical logic observers for finite automata. In Proceedings of 27th Conference on Decision and Control, pages 226–233, Austin, TX, 1988.
P. M. Frank. Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy-a survey and some new results. Automatica, 26(3):459–474, 1990.
Y. Liu. Switching observer design for uncertain nonlinear systems. IEEE Trans. on Automatic Control, 42(1):1699–1703, 1997.
C. Van Loan. The sensitivity of the matrix exponential. SIAM Journal of Number Analysis, 14(6):971–981, December 1977.
D.G. Luenberger. An introduction to observers. IEEE Transactions on Automatic Control, 16(6):596–602, Dec 1971.
M.-A. Massoumnia, G.C., Verghese, and A.S. Willsky. Failure detection and identification. IEEE Transactions on Automatic Control, 34(3):316–21, March 1989.
C. M. Özveren and A. S. Willsky. Observability of discrete event dynamic systems. IEEE Trans. on Automatic Control, 35:797–806, 1990.
C. M. Özveren, A. S. Willsky, and P. J. Antsaklis. Stability and stabilizability of discrete event dynamic systems. Journal of the Association for Computing Machinery, 38:730–752, 1991.
P. J. Ramadge. Observability of discrete event-systems. In Proceedings of 25th Conference on Decision and Control, pages 1108–1112, Athens, Greece, 1986.
M. Vidyasagar. Nonlinear Systems Analysis. Prentice-Hall, Inc, Englewood Cliffs, N.J., 1978.
H. Ye, A. N. Michel, and L. Hou. Stability theory for hybrid dynamical systems for switched and hybrid systems. IEEE Trans. on Automatic Control, 43(4):461–474, 1998.
Q. Zhang. Hybrid filtering for linear systems with non-baussian disturbances. IEEE Trans. on Automatic Control, 45(1):50–61, 1999.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Balluchi, A., Benvenuti, L., Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (2002). Design of Observers for Hybrid Systems. In: Tomlin, C.J., Greenstreet, M.R. (eds) Hybrid Systems: Computation and Control. HSCC 2002. Lecture Notes in Computer Science, vol 2289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45873-5_9
Download citation
DOI: https://doi.org/10.1007/3-540-45873-5_9
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43321-7
Online ISBN: 978-3-540-45873-9
eBook Packages: Springer Book Archive