Explicit Euler Discretization of an Indirect Adaptive Sliding Mode Control

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

doi:10.1109/VSS57184.2022.9902081

Explicit Euler Discretization of an Indirect Adaptive Sliding Mode Control

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

^*Corresponding author for this work

Institute of Automation and Control (4430)

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

Abstract

In this paper, an explicit Euler discretization scheme is used to obtain a discrete-time version of the indirect adaptive sliding mode control for an uncertain scalar linear system with an unknown parameter. The unknown parameter is linear in the state, the input disturbance is assumed to be bounded. An improper discretization of indirect adaptive sliding mode algorithms may lead to unbounded parameter estimates, which then result in an unbounded state. We modify the algorithm by using a priori knowledge of the location of the unknown parameter such that boundedness of the trajectory can be guaranteed. This entails obtaining a stabilizing condition on the sampling interval and calculating the bound of the state trajectory. The proposed discretization is illustrated by simulation results of an academic scalar system.

Original language	English
Title of host publication	2022 16th International Workshop on Variable Structure Systems, VSS 2022
Publisher	Institute of Electrical and Electronics Engineers
Pages	278-283
Number of pages	6
ISBN (Electronic)	9781665463591
DOIs	https://doi.org/10.1109/VSS57184.2022.9902081
Publication status	Published - 2022
Event	16th International Workshop on Variable Structure Systems and Sliding Mode Control: VSS 2022 - Rio de Janeiro, Brazil Duration: 11 Sept 2022 → 14 Sept 2022

Publication series

Name	Proceedings of IEEE International Workshop on Variable Structure Systems
Volume	2022-September
ISSN (Print)	2165-4816
ISSN (Electronic)	2165-4824

Conference

Conference	16th International Workshop on Variable Structure Systems and Sliding Mode Control
Abbreviated title	VSS 2022
Country/Territory	Brazil
City	Rio de Janeiro
Period	11/09/22 → 14/09/22

ASJC Scopus subject areas

Electrical and Electronic Engineering
Control and Systems Engineering

Fields of Expertise

Information, Communication & Computing

Access to Document

10.1109/VSS57184.2022.9902081

Cite this

Hettiger, C., Kumari, K., Watermann, L., Eisenzopf, L., Weissenberger, F., Horn, M., Koch, S., Reger, J., & Reichhartinger, M. (2022). Explicit Euler Discretization of an Indirect Adaptive Sliding Mode Control. In 2022 16th International Workshop on Variable Structure Systems, VSS 2022 (pp. 278-283). (Proceedings of IEEE International Workshop on Variable Structure Systems; Vol. 2022-September). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/VSS57184.2022.9902081

Explicit Euler Discretization of an Indirect Adaptive Sliding Mode Control. / Hettiger, Christina; Kumari, Kiran; Watermann, Lars et al.
2022 16th International Workshop on Variable Structure Systems, VSS 2022. Institute of Electrical and Electronics Engineers, 2022. p. 278-283 (Proceedings of IEEE International Workshop on Variable Structure Systems; Vol. 2022-September).

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

Hettiger, C, Kumari, K, Watermann, L, Eisenzopf, L, Weissenberger, F, Horn, M , Koch, S, Reger, J & Reichhartinger, M 2022, Explicit Euler Discretization of an Indirect Adaptive Sliding Mode Control. in 2022 16th International Workshop on Variable Structure Systems, VSS 2022. Proceedings of IEEE International Workshop on Variable Structure Systems, vol. 2022-September, Institute of Electrical and Electronics Engineers, pp. 278-283, 16th International Workshop on Variable Structure Systems and Sliding Mode Control, Rio de Janeiro, Brazil, 11/09/22. https://doi.org/10.1109/VSS57184.2022.9902081

Hettiger C, Kumari K, Watermann L, Eisenzopf L, Weissenberger F, Horn M et al. Explicit Euler Discretization of an Indirect Adaptive Sliding Mode Control. In 2022 16th International Workshop on Variable Structure Systems, VSS 2022. Institute of Electrical and Electronics Engineers. 2022. p. 278-283. (Proceedings of IEEE International Workshop on Variable Structure Systems). doi: 10.1109/VSS57184.2022.9902081

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AU - Horn, Martin

AU - Koch, Stefan

AU - Reger, Johann

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AB - In this paper, an explicit Euler discretization scheme is used to obtain a discrete-time version of the indirect adaptive sliding mode control for an uncertain scalar linear system with an unknown parameter. The unknown parameter is linear in the state, the input disturbance is assumed to be bounded. An improper discretization of indirect adaptive sliding mode algorithms may lead to unbounded parameter estimates, which then result in an unbounded state. We modify the algorithm by using a priori knowledge of the location of the unknown parameter such that boundedness of the trajectory can be guaranteed. This entails obtaining a stabilizing condition on the sampling interval and calculating the bound of the state trajectory. The proposed discretization is illustrated by simulation results of an academic scalar system.

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Explicit Euler Discretization of an Indirect Adaptive Sliding Mode Control

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