On Discretization Methods for Indirect Adaptive Sliding Mode Control

Christina Hettiger; Lars Watermann; Kiran Kumari; Lukas Eisenzopf; Florian Weissenberger; Martin Horn; Stefan Koch; Johann Reger; Markus Reichhartinger

doi:10.1109/CDC51059.2022.9993161

On Discretization Methods for Indirect Adaptive Sliding Mode Control

Christina Hettiger, Lars Watermann, Kiran Kumari, Lukas Eisenzopf, Florian Weissenberger, Martin Horn, Stefan Koch, Johann Reger, Markus Reichhartinger

Institute of Automation and Control (4430)

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

Abstract

In this paper, discrete-time versions of the first-order indirect adaptive sliding mode control (SMC) algorithm are developed and analyzed. In particular, a scalar linear system with parametric uncertainty linear in the state and with bounded input disturbance is considered. The discretization of continuous-time first-order indirect adaptive SMC algorithm may not preserve continuous-time properties like asymptotic stability of the origin. In order to ensure boundedness, knowledge about where the actual parameter may be located is used in this work. Then, for each proposed discretization scheme, conditions on the sampling time are derived that guarantee convergence into a bounded set. The theoretical results are illustrated with simulation examples and the proposed discretization schemes are compared with regard to the condition on sampling time and precision

Original language	English
Title of host publication	2022 IEEE 61st Conference on Decision and Control, CDC 2022
Pages	4930-4936
Number of pages	7
ISBN (Electronic)	9781665467612
DOIs	https://doi.org/10.1109/CDC51059.2022.9993161
Publication status	Published - Jan 2023
Event	2022 61th IEEE Conference on Decision and Control: CDC 2022 - Cancún, Mexico Duration: 6 Dec 2022 → 9 Dec 2022 Conference number: 61 https://cdc2022.ieeecss.org/

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2022-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	2022 61th IEEE Conference on Decision and Control
Abbreviated title	CDC 2022
Country/Territory	Mexico
City	Cancún
Period	6/12/22 → 9/12/22
Internet address	https://cdc2022.ieeecss.org/

ASJC Scopus subject areas

Control and Optimization
Control and Systems Engineering
Modelling and Simulation

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10.1109/CDC51059.2022.9993161

Cite this

Hettiger, C., Watermann, L., Kumari, K., Eisenzopf, L., Weissenberger, F., Horn, M., Koch, S., Reger, J., & Reichhartinger, M. (2023). On Discretization Methods for Indirect Adaptive Sliding Mode Control. In 2022 IEEE 61st Conference on Decision and Control, CDC 2022 (pp. 4930-4936). (Proceedings of the IEEE Conference on Decision and Control; Vol. 2022-December). https://doi.org/10.1109/CDC51059.2022.9993161

On Discretization Methods for Indirect Adaptive Sliding Mode Control. / Hettiger, Christina; Watermann, Lars; Kumari, Kiran et al.
2022 IEEE 61st Conference on Decision and Control, CDC 2022. 2023. p. 4930-4936 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2022-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

Hettiger, C, Watermann, L, Kumari, K, Eisenzopf, L, Weissenberger, F, Horn, M , Koch, S, Reger, J & Reichhartinger, M 2023, On Discretization Methods for Indirect Adaptive Sliding Mode Control. in 2022 IEEE 61st Conference on Decision and Control, CDC 2022. Proceedings of the IEEE Conference on Decision and Control, vol. 2022-December, pp. 4930-4936, 2022 61th IEEE Conference on Decision and Control, Cancún, Mexico, 6/12/22. https://doi.org/10.1109/CDC51059.2022.9993161

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abstract = "In this paper, discrete-time versions of the first-order indirect adaptive sliding mode control (SMC) algorithm are developed and analyzed. In particular, a scalar linear system with parametric uncertainty linear in the state and with bounded input disturbance is considered. The discretization of continuous-time first-order indirect adaptive SMC algorithm may not preserve continuous-time properties like asymptotic stability of the origin. In order to ensure boundedness, knowledge about where the actual parameter may be located is used in this work. Then, for each proposed discretization scheme, conditions on the sampling time are derived that guarantee convergence into a bounded set. The theoretical results are illustrated with simulation examples and the proposed discretization schemes are compared with regard to the condition on sampling time and precision",

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AU - Koch, Stefan

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AB - In this paper, discrete-time versions of the first-order indirect adaptive sliding mode control (SMC) algorithm are developed and analyzed. In particular, a scalar linear system with parametric uncertainty linear in the state and with bounded input disturbance is considered. The discretization of continuous-time first-order indirect adaptive SMC algorithm may not preserve continuous-time properties like asymptotic stability of the origin. In order to ensure boundedness, knowledge about where the actual parameter may be located is used in this work. Then, for each proposed discretization scheme, conditions on the sampling time are derived that guarantee convergence into a bounded set. The theoretical results are illustrated with simulation examples and the proposed discretization schemes are compared with regard to the condition on sampling time and precision

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On Discretization Methods for Indirect Adaptive Sliding Mode Control

Abstract

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