×
Mullari, Tanel; Kotta, Ülle

Feedback linearization of discrete-time nonlinear control systems: computational aspects. (English) Zbl 1467.93063

Proc. Est. Acad. Sci. 69, No. 1, 11-26 (2020).
Summary: An alternative solution of the static state feedback linearization problem for the discrete-time case is given. This solution is based on the sequence of distributions, whose computation requires only the knowledge of the backward shift equations. This computational method is especially suitable for the class of discrete-time systems, obtained from the implicit Euler discretization of continuous-time systems. As a practical example the implicit Euler discretization of hydraulic press equations is considered.

MSC:

93B18 Linearizations
93B52 Feedback control
93C55 Discrete-time control/observation systems
93C10 Nonlinear systems in control theory
93-08 Computational methods for problems pertaining to systems and control theory

Keywords:

feedback linearizability; discrete-time systems; vector fields; implicit Euler method

Software:

Maple
Cite Review PDF
Full Text: DOI
OA License

References:

[1] Jakubczyk, B. Feedback linearization of discrete-time systems. Syst. Control Lett., 1987, 9(5), 411-416. · Zbl 0632.93034 · doi:10.1016/0167-6911(87)90070-3
[2] Grizzle, W. Feedback linearization of discrete-time systems. Lecture Notes Contr. Inform. Sci., 1986, 83, 273-281. · doi:10.1007/BFb0007564
[3] Aranda-Bricaire,E.,Kotta,Ü.,and Moog,C.H. Linearization of discrete-time systems. SIAMJ. Control. Optim., 1996, 34(6), 1999-2023. · Zbl 0863.93014 · doi:10.1137/S0363012994267315
[4] Califano, C., Monaco, S., and Normand-Cyrot, D. On the problem of feedback linearization. Syst. Control Lett., 1999, 36(1), 61-67. · Zbl 0913.93011 · doi:10.1016/S0167-6911(98)00070-X
[5] Mullari, T., Kotta, Ü., Bartosiewicz, Z., Pawluszewicz, E., and Moog, C. H. Forward and backward shifts of vector fields: towards the dual algebraic framework. IEEE Trans. Autom. Control, 2017, 62(6) 3029-3033. · Zbl 1369.93147 · doi:10.1109/TAC.2016.2608718
[6] Mullari, T. and Schlacher, K. Geometric control for a nonlinear sampled data system. In MTNS 2014: 21st International Symposium of Mathematical Theory of Networks and Systems, July 7-11, 2014, Groningen, the Netherlands, Proceedings. University of Groningen, Groningen, 2014, 54-61.
[7] Nam, K. Linearization of discrete-time nonlinear systems and a canonical structure. IEEE Trans. Autom. Control, 1989, 34, 119-211. · Zbl 0663.93013 · doi:10.1109/9.8665
[8] Jayaraman, G. and Chizek, H. J. Feedback linearization of discrete-time systems. In Proceedings of the 32nd IEEE CDC. San Antonio, 1993, 2972-2977.
[9] Kotta, Ü., Tõnso, M., Shumsky, A. Y., and Zhirabok, Z. N. Feedback linearization and lattice theory. Syst. Control Lett., 2013, 62(3), 248-255. · Zbl 1261.93034
[10] Simões, C. and Nijmeijer, H. Nonsmooth stabilizability and feedback linearization of discrete-time nonlinear systems. Int. J. Robust Nonlinear Control, 1996, 6(3), 171-188. · Zbl 0853.93090 · doi:10.1002/(SICI)1099-1239(199604)6:3%3c171::AID-RNC140%3e3.0.CO;2-0
[11] Kaldmäe, A., Kotta,Ü., Shumsky,A.,and Zhirabok, A. Feedback linearization of possible non-smooth systems. Proc. Estonian Acad. Sci., 2017, 66(2), 109-123. · Zbl 1382.93012 · doi:10.3176/proc.2017.2.01
[12] Efimov, D., Polyakov, A., Levant, A., and Perruquetti, W. Realization and discretization of asymptotically stable homogenous systems. IEEE Trans. Autom. Control, 2017, 62(11), 5962-5969. · Zbl 1396.65109 · doi:10.1109/TAC.2017.2699284
[13] Belikov, J., Kaldmäe, A., and Kotta, Ü. Global linearization approach to nonlinear control systems: a brief tutorial overview. Proc. Estonian Acad. Sci., 2017, 66(3), 243-263. · Zbl 1386.93077 · doi:10.3176/proc.2017.3.01
[14] Kotta, Ü. Discrete-time models of a nonlinear continuous-time system. Proc. Estonian Acad. Sci. Phys. Math., 1994, 43(1), 64-78. · Zbl 0836.93034
[15] Kotta, Ü., Liu, P., and Zinober, A. S. I. Transfer equivalence and realization of nonlinear higher order i/o difference equations using Maple. In Proceedings of the 4th IFAC World Congress, Vol. E (Chen, H.-F. et al., eds). Pergamon, Beijing, Oxford, 1999, 249-254.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.