Disturbance decoupling of multi-input multi-output discrete-time nonlinear systems by static measurement feedback; pp. 77–88Full article in PDF format | doi: 10.3176/proc.2012.2.01
This paper addresses the disturbance decoupling problem (DDP) for nonlinear systems, extending the results for continuous-time systems into the discrete-time case. Sufficient conditions are given for the solvability of the problem. The notion of the rank of a one-form is used to find the static measurement feedback that solves the DDP whenever possible. Moreover, necessary and sufficient conditions are given for single-input single-output systems, as well as for multi-input multi-output systems under the additional assumption.
1. Andiarti, R. and Moog, C. H. Output feedback disturbance decoupling in nonlinear systems. IEEE Trans. Autom. Control, 1996, 41, 1683–1689.
2. Aranda-Bricaire, E. and Kotta, Ü. Generalized controlled invariance for discrete-time nonlinear systems with application to the dynamic disturbance problem. IEEE Trans. Autom. Control, 2001, 46, 165–171.
3. Aranda-Bricaire, E. and Kotta, Ü. A geometric solution to the dynamic disturbance decoupling for discrete-time nonlinear systems. Kybernetika, 2004, 49, 197–206.
4. Aranda-Bricaire, E., Kotta, Ü., and Moog, C. H. Linearization of discrete-time systems. SIAM J. Control Optim.}, 1996, 6, 1999–2023.
5. Choquet-Bruhat, Y., DeWitt-Morette, C., and Dillard-Bleick, M. Analysis, Manifolds and Physics. Elsevier, 1996.
6. Conte, G., Moog, C. H., and Perdon, A. M. Algebraic Methods for Nonlinear Control Systems. Theory and Applications. Springer, 2007.
7. Fliegner, T. and Nijmeijer, H. Dynamic disturbance decoupling of nonlinear discrete-time systems. In Proceedings of the 33rd IEEE Conference on Decision and Control, vol. 2. 1994, 1790–1791.
8. Grizzle, J. W. Controlled invariance for discrete-time nonlinear systems with an application to the disturbance decoupling problem. IEEE Trans. Autom. Control, 1985, 30, 868–873.
9. Halas, M., Kotta, Ü., Li, Z., Wang, H., and Yuan, C. Submersive rational difference systems and their accessibility. In Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, Seoul, Korea. 2009, 175–182.
10. Isidori, A. Nonlinear Control Systems. Springer, London, 1995.
11. Isidori, A., Krener, A. J., Gori-Giorgi, C., and Monaco, S. Nonlinear decoupling via feedback: a differential geometric approach. IEEE Trans. Autom. Control, 1981, 26, 331–345.
12. Kaldmäe, A. and Kotta, Ü. Disturbance decoupling of discrete-time nonlinear systems by static
measurement feedback. In Proceedings of the 18th International Conference on Process Control (Fikar, M. and Kvasnica, M., eds). Tatranská Lomnica, Slovakia. 2011, 135–140.
13. Kotta, Ü. and Mullari, T. Discussion on: “Unified approach to the problem of full decoupling via output feedback”. European J. Control, 2010, 16(4), 326–328.
14. Kotta, Ü. and Nijmeijer, H. Dynamic disturbance decoupling for nonlinear discrete-time systems. Proc. Acad. Sci. USSR, Technical Cybernetics, 1991, 4, 52–59 (in Russian).
15. Kotta, Ü., Shumsky, A. Ye., and Zhirabok, A. N. Output feedback disturbance decoupling in discrete-time nonlinear systems. In Proceedings of the 18th IFAC World Congress, Milano, Italy. 2011, 239–244.
16. Monaco, S. and Normand-Cyrot, D. Invariant distributions for discrete-time nonlinear systems. Syst. Control Lett., 1984, 5, 191–196.
17. Nijmeijer, H. and van der Schaft, A. J. Nonlinear Dynamical Control Systems. Springer, New York, 1990.
18. Pothin, R. and Moog, C. H. Measurement feedback disturbance decoupling of nonlinear discrete-time systems. In Proceedings of the 5th IFAC Symposium on Nonlinear Control Systems, St. Petersburg. 2001, 1271–1274.
19. Pothin, R., Moog, C. H., and Xia, X. Disturbance decoupling of nonlinear MISO systems by static measurement feedback. Kybernetika, 2002, 38, 601–608.
20. Shumsky, A. Ye. and Zhirabok, A. N. Unified approach to the problem of full decoupling via output feedback. European J. Control, 2010, 16(4), 313–325.
21. Xia, X. and Moog, C. H. Disturbance decoupling by measurement feedback for SISO nonlinear systems. IEEE Trans. Autom. Control, 1999, 44, 1425–1429.
22. Zhirabok, A. N. and Shumsky, A. Ye. The Algebraic Methods for Analysis of Nonlinear Dynamic Systems. Dalnauka, Vladivostok, 2008 (in Russian).
Back to Issue