Sliding mode control to stabilization of a fractional ODE and a fractional PDE cascaded systems subject to disturbances

Jiake Sun; Junmin Wang

doi:10.1109/CCDC58219.2023.10327437

Sliding mode control to stabilization of a fractional ODE and a fractional PDE cascaded systems subject to disturbances

Jiake Sun^*, Junmin Wang

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

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

1 Citation (Scopus)

Abstract

In this paper, we consider the input-to-state stabilization of a fractional-order ODE-PDE cascaded system with disturbances in all channels. By applying the backstepping method and sliding mode control approach, we design a discontinuous feedback control to reject the matched disturbances. The existence of the generalized solution of the closed-loop system is proved by Galerkin's method. The input-to-state Mittag-Leffler stability of closed-loop system is proven by Lyapunov method. Finally, we present some numerical simulations to show the correctness of the theoretical results.

Original language	English
Title of host publication	Proceedings of the 35th Chinese Control and Decision Conference, CCDC 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	383-388
Number of pages	6
ISBN (Electronic)	9798350334722
DOIs	https://doi.org/10.1109/CCDC58219.2023.10327437
Publication status	Published - 2023
Event	35th Chinese Control and Decision Conference, CCDC 2023 - Yichang, China Duration: 20 May 2023 → 22 May 2023

Publication series

Name	Proceedings of the 35th Chinese Control and Decision Conference, CCDC 2023

Conference

Conference	35th Chinese Control and Decision Conference, CCDC 2023
Country/Territory	China
City	Yichang
Period	20/05/23 → 22/05/23

Keywords

backstepping method
fractional-order cascaded system
input-to-state stability
sliding mode control

Access to Document

10.1109/CCDC58219.2023.10327437

Cite this

Sun, J., & Wang, J. (2023). Sliding mode control to stabilization of a fractional ODE and a fractional PDE cascaded systems subject to disturbances. In Proceedings of the 35th Chinese Control and Decision Conference, CCDC 2023 (pp. 383-388). (Proceedings of the 35th Chinese Control and Decision Conference, CCDC 2023). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CCDC58219.2023.10327437

Sun, Jiake ; Wang, Junmin. / Sliding mode control to stabilization of a fractional ODE and a fractional PDE cascaded systems subject to disturbances. Proceedings of the 35th Chinese Control and Decision Conference, CCDC 2023. Institute of Electrical and Electronics Engineers Inc., 2023. pp. 383-388 (Proceedings of the 35th Chinese Control and Decision Conference, CCDC 2023).

@inproceedings{c35504e4be204a7885c8a9bc26419781,

title = "Sliding mode control to stabilization of a fractional ODE and a fractional PDE cascaded systems subject to disturbances",

abstract = "In this paper, we consider the input-to-state stabilization of a fractional-order ODE-PDE cascaded system with disturbances in all channels. By applying the backstepping method and sliding mode control approach, we design a discontinuous feedback control to reject the matched disturbances. The existence of the generalized solution of the closed-loop system is proved by Galerkin's method. The input-to-state Mittag-Leffler stability of closed-loop system is proven by Lyapunov method. Finally, we present some numerical simulations to show the correctness of the theoretical results.",

keywords = "backstepping method, fractional-order cascaded system, input-to-state stability, sliding mode control",

author = "Jiake Sun and Junmin Wang",

note = "Publisher Copyright: {\textcopyright} 2023 IEEE.; 35th Chinese Control and Decision Conference, CCDC 2023 ; Conference date: 20-05-2023 Through 22-05-2023",

year = "2023",

doi = "10.1109/CCDC58219.2023.10327437",

language = "English",

series = "Proceedings of the 35th Chinese Control and Decision Conference, CCDC 2023",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "383--388",

booktitle = "Proceedings of the 35th Chinese Control and Decision Conference, CCDC 2023",

address = "United States",

}

Sun, J & Wang, J 2023, Sliding mode control to stabilization of a fractional ODE and a fractional PDE cascaded systems subject to disturbances. in Proceedings of the 35th Chinese Control and Decision Conference, CCDC 2023. Proceedings of the 35th Chinese Control and Decision Conference, CCDC 2023, Institute of Electrical and Electronics Engineers Inc., pp. 383-388, 35th Chinese Control and Decision Conference, CCDC 2023, Yichang, China, 20/05/23. https://doi.org/10.1109/CCDC58219.2023.10327437

Sliding mode control to stabilization of a fractional ODE and a fractional PDE cascaded systems subject to disturbances. / Sun, Jiake; Wang, Junmin.
Proceedings of the 35th Chinese Control and Decision Conference, CCDC 2023. Institute of Electrical and Electronics Engineers Inc., 2023. p. 383-388 (Proceedings of the 35th Chinese Control and Decision Conference, CCDC 2023).

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

TY - GEN

T1 - Sliding mode control to stabilization of a fractional ODE and a fractional PDE cascaded systems subject to disturbances

AU - Sun, Jiake

AU - Wang, Junmin

PY - 2023

Y1 - 2023

N2 - In this paper, we consider the input-to-state stabilization of a fractional-order ODE-PDE cascaded system with disturbances in all channels. By applying the backstepping method and sliding mode control approach, we design a discontinuous feedback control to reject the matched disturbances. The existence of the generalized solution of the closed-loop system is proved by Galerkin's method. The input-to-state Mittag-Leffler stability of closed-loop system is proven by Lyapunov method. Finally, we present some numerical simulations to show the correctness of the theoretical results.

AB - In this paper, we consider the input-to-state stabilization of a fractional-order ODE-PDE cascaded system with disturbances in all channels. By applying the backstepping method and sliding mode control approach, we design a discontinuous feedback control to reject the matched disturbances. The existence of the generalized solution of the closed-loop system is proved by Galerkin's method. The input-to-state Mittag-Leffler stability of closed-loop system is proven by Lyapunov method. Finally, we present some numerical simulations to show the correctness of the theoretical results.

KW - backstepping method

KW - fractional-order cascaded system

KW - input-to-state stability

KW - sliding mode control

UR - http://www.scopus.com/inward/record.url?scp=85181797756&partnerID=8YFLogxK

U2 - 10.1109/CCDC58219.2023.10327437

DO - 10.1109/CCDC58219.2023.10327437

M3 - Conference contribution

AN - SCOPUS:85181797756

T3 - Proceedings of the 35th Chinese Control and Decision Conference, CCDC 2023

SP - 383

EP - 388

BT - Proceedings of the 35th Chinese Control and Decision Conference, CCDC 2023

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 35th Chinese Control and Decision Conference, CCDC 2023

Y2 - 20 May 2023 through 22 May 2023

ER -

Sun J, Wang J. Sliding mode control to stabilization of a fractional ODE and a fractional PDE cascaded systems subject to disturbances. In Proceedings of the 35th Chinese Control and Decision Conference, CCDC 2023. Institute of Electrical and Electronics Engineers Inc. 2023. p. 383-388. (Proceedings of the 35th Chinese Control and Decision Conference, CCDC 2023). doi: 10.1109/CCDC58219.2023.10327437

Sliding mode control to stabilization of a fractional ODE and a fractional PDE cascaded systems subject to disturbances

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