| Title:
|
Structurally stable design of output regulation for a class of nonlinear systems (English) |
| Author:
|
Villanueva-Novelo, Celia |
| Author:
|
Čelikovský, Sergej |
| Author:
|
Castillo-Toledo, Bernardino |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
37 |
| Issue:
|
5 |
| Year:
|
2001 |
| Pages:
|
[547]-564 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The problem of output regulation of the systems affected by unknown constant parameters is considered here. The main goal is to find a unique feedback compensator (independent on the actual values of unknown parameters) that drives a given error (control criterion) asymptotically to zero for all values of parameters from a certain neighbourhood of their nominal value. Such a task is usually referred to as the structurally stable output regulation problem. Under certain assumptions, such a problem is known to be solvable using dynamical error feedback. The corresponding necessary and sufficient conditions basically include the solvability of the so-called regulator equation and the existence of an immersion of a certain system with outputs into the one having favourable observability and controllability properties. Its model is then directly used for dynamic compensator construction. Usually, such an immersion may be selected as the one to an observable linear system with outputs. In a general case, the above mentioned conditions are highly nonconstructive and difficult to check. This paper studies a certain particular class of systems, the so-called strictly triangular polynomial systems, where that immersion to a linear system can be obtained in a constructive way. Moreover, it provides computer algorithm (based on MAPLE symbolic package) to design the corresponding solution to the structurally stable output regulation problem. Examples together with computer simulations are included to clarify the suggested approach. (English) |
| Keyword:
|
nonlinear system |
| Keyword:
|
stable output regulation |
| MSC:
|
93B07 |
| MSC:
|
93B51 |
| MSC:
|
93C10 |
| MSC:
|
93D15 |
| MSC:
|
93D20 |
| MSC:
|
93D25 |
| idZBL:
|
Zbl 1265.93218 |
| idMR:
|
MR1877073 |
| . |
| Date available:
|
2009-09-24T19:41:36Z |
| Last updated:
|
2015-03-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135426 |
| . |
| Reference:
|
[1] Byrnes C. I., Priscolli, F. Delli, Isidori A.: Output Regulation of Uncertain Nonlinear Systems.Birkhäuser, Boston 1997 MR 1438783 |
| Reference:
|
[2] Čelikovský S.: Local stabilization and controllability of a class of nontriangular nonlinear systems.In: Proc. 36th IEEE Conference on Decision and Control, San Diego 1997, pp. 1728–1733 |
| Reference:
|
[3] Čelikovský S., Huang J.: Continuous feedback asymptotic output regulation for a class of nonlinear systems having nonstabilizable linearization.In: Proc. 37th IEEE Conference on Decision and Control, Tampa 1999, pp. 3087–3092 |
| Reference:
|
[4] Čelikovský S., Huang J.: Continuous feedback practical output regulation for a class of nonlinear systems having nonstabilizable linearization.In: Proc. 38th IEEE Conference on Decision and Control, Phoenix 2000, pp. 4796–4801 |
| Reference:
|
[5] Chen, Ch.: Linear System Theory and Design.Third edition. Oxford University Press, Oxford 1984 |
| Reference:
|
[6] Guckenheimer J., Holmes P.: Nonlinear Oscilations, Dynamical Systems and Bifurcations of Vector Fields.Springer–Verlag, New York 1983 MR 0709768 |
| Reference:
|
[7] Huang J., Rugh W. J.: On a nonlinear multivariable servomechanism problem.Automatica 26 (1990), 963–972 Zbl 0717.93019, MR 1080983, 10.1016/0005-1098(90)90081-R |
| Reference:
|
[8] Huang J.: Asymptotic tracking and disturbance rejection in uncertain nonlinear system.IEEE Trans. Automat. Control 40 (1995), 1118–1122 MR 1345975, 10.1109/9.388697 |
| Reference:
|
[9] Isidori A.: Nonlinear Control Systems.Third edition. Springer–Verlag, New York 1995, pp. 385–425 Zbl 0878.93001, MR 1410988 |
| Reference:
|
[10] Isidori A., Byrnes C. I.: Output Regulation of nonlinear systems.IEEE Trans. Automat. Control 35 (1990), 131–140 Zbl 0704.93034, MR 1038409, 10.1109/9.45168 |
| Reference:
|
[11] Knobloch H., al A. Isidori et: Topics in Control Theory.Birkhäuser, Boston 1993 Zbl 0789.93073, MR 1284714 |
| Reference:
|
[12] Marino R., Tomei P.: Nonlinear Control Design – Nonlinear, Robust and Adaptive.Prentice Hall, Englewood Cliffs, N.Y. 1994 |
| . |
