Previous |  Up |  Next


input-output decoupling problem; nonlinear input-output model
The input-output decoupling problem is studied for a class of recursive nonlinear systems (RNSs), i. e. for systems, modelled by higher order nonlinear difference equations, relating the input, the output and a finite number of their time shifts. The solution of the problem via regular static feedback known for discrete-time nonlinear systems in state space form, is extended to RNSs. Necessary and sufficient conditions for local solvability of the problem are proposed. This is the alternative to be used when some nonlinear input-outpt models cannot be realized in the state-space form.
[1] Bastin G., Jarachi F., Mareels I. M. Y.: Dead beat control of recursive nonlinear systems. In: Proc. of the 32nd Conference on Decision and Control, San Antonio 1993, pp. 2965–2971
[2] Chen S., Billings S. A.: Representation of non–linear systems: the NARMAX model. Internat. J. Control 49 (1989), 1013–1032 DOI 10.1080/00207178908559683 | MR 0990327
[3] Fliess M.: Automatique en temps discret et algèbre aux différences. Forum Math. 2 (1990), 213–232 DOI 10.1515/form.1990.2.213 | MR 1050406 | Zbl 0706.93039
[4] Hammer J.: Nonlinear systems: stability and rationality. Internat. J. Control 40 (1984), 1–35 DOI 10.1080/00207178408933254 | MR 0750409
[5] Isidori A.: Nonlinear Control Systems. Second edition. Springer–Verlag, Berlin 1989 MR 1015932 | Zbl 0931.93005
[6] Kotta Ü.: Inversion Method in the Discrete–time Nonlinear Control Systems Synthesis Problems. Springer–Verlag, London 1995 MR 1338376 | Zbl 0822.93001
[7] Kotta Ü.: On right invertibility of recursive nonlinear systems. In: Proc. of the 13th IFAC World Congress, San Fransisco 1996 MR 1430762
[8] Kotta Ü.: Model matching problem for nonlinear recursive systems. Proc. Estonian Acad. Sci. Phys. Math. 46 (1997), 251–261 MR 1487063 | Zbl 0911.93013
[9] Kotta Ü., Liu P., Zinober A. S. I.: State-space realization of input–output nonlinear difference equations. In: Proc. of European Control Conference, Brussels 1997, Paper N 851 (CD–ROM)
[10] Levin A. U., Narendra K. S.: Recursive identification using feedforward neural networks. Internat. J. Control 61 (1995), 533–547 DOI 10.1080/00207179508921916 | MR 1617011 | Zbl 0830.93017
[11] Levin A. U., Narendra K. S.: Control of nonlinear dynamical systems using neural networks. Part 2: Observabiliy, identification, and control. IEEE Trans. Neural Networks 7 (1996), 30–42 DOI 10.1109/72.478390
[12] Narendra K. S., Cabrera J. B. D.: Input–output representation of discrete–time dynamical systems – nonlinear ARMA models. In: Proc. of the 33rd Conference on Decision and Control, 1994, pp. 1118–1119
[13] Nijmeijer H., Schaft A. J. van der: Nonlinear Dynamical Control Systems. Springer–Verlag, New York 1990 MR 1047663
Partner of
EuDML logo