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Lyapunov based continuous-time nonlinear controller redesign for sampled-data implementation

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005520
URN to cite this document: urn:nbn:de:bvb:703-epub-5520-5

Title data

Nešić, Dragan ; Grüne, Lars:
Lyapunov based continuous-time nonlinear controller redesign for sampled-data implementation.
Bayreuth , 2004

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Abstract

Given a continuous-time controller and a Lyapunov function that shows global asymptotic stability for the closed loop system, we provide several results for modification of the controller for sampled-data implementation. The main idea behind this approach is to use a particular structure for the redesigned controller and the main technical result is to show that the Fliess series expansions (in the sampling period T) of the Lyapunov difference for the sampled-data system with the redesigned controller have a very special form that is useful for controller redesign. We present results on controller redesign that achieve two different goals. The first goal is making the lower order terms (in T) in the series expansion of the Lyapunov difference with the redesigned controller more negative. These control laws are very similar to those obtained from Lyapunov based redesign of continuous-time systems for robustification of control laws and they often lead to corrections of the well known "-LgV" form. The second goal is making the lower order terms (in T) in the Fliess expansions of the Lyapunov difference for the sampled-data system with the redesigned controller behave as close as possible to the lower order terms of the Lyapunov difference along solutions of the "ideal" sampled response of the continuous-time system with the original controller. In this case, the controller correction is very different from the first case and it contains appropriate "prediction" terms. The method is very flexible and one may try to achieve other objectives not addressed in this paper or derive similar results under different conditions. Simulation studies verify that redesigned controllers perform better (in an appropriate sense) than the unmodified ones when they are digitally implemented with sufficiently small sampling period T.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): erschienen In:
Automatica. Bd. 41 (2005) Heft 7 . - S. 1143-1156
Keywords: Nonlinear sampled data systems; Controller design; Lyapunov function
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-5520-5
Date Deposited: 17 May 2021 11:27
Last Modified: 17 May 2021 11:27
URI: https://epub.uni-bayreuth.de/id/eprint/5520

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