Fuzzy Boundary Control for Nonlinear Delayed DPSs under Boundary Measurements

Zi Peng Wang; Xu Zhang; Huai Ning Wu; Tingwen Huang

doi:10.1109/TCYB.2021.3105249

Fuzzy Boundary Control for Nonlinear Delayed DPSs under Boundary Measurements

Zi Peng Wang^*
, Xu Zhang
, Huai Ning Wu
, Tingwen Huang

^*Corresponding author for this work

School of Automation Science and Electrical Engineering

University of Jinan
Texas A&M University

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

For nonlinear delayed distributed parameter systems (DDPSs), this article considers a fuzzy boundary control (FBC) under boundary measurements (BMs). Initially, we accurately describe the nonlinear DDPS through a Takagi-Sugeno (T-S) fuzzy partial differential-difference equation (PDDE). Then, in accordance with the T-S fuzzy PDDE model, an FBC design under BMs ensuring the exponential stability for closed-loop DDPS is subsequently presented by spatial linear matrix inequalities (SLMIs) via using Wirtinger's inequality, Halanay's inequality, and the Lyapunov direct method, which respects the fast-varying and slow-varying delays. Moreover, we formulate SLMIs as LMIs for solving the fuzzy boundary controller design of nonlinear DDPSs under BMs. Finally, the effectiveness of the proposed FBC strategy is presented via simulation examples.

Original language	English
Pages (from-to)	1547-1556
Number of pages	10
Journal	IEEE Transactions on Cybernetics
Volume	53
Issue number	3
DOIs	https://doi.org/10.1109/TCYB.2021.3105249
State	Published - 1 Mar 2023

Keywords

Boundary measurements (BMs)
delayed distributed parameter systems (DDPSs)
fuzzy boundary control (FBC)

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10.1109/TCYB.2021.3105249

Cite this

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title = "Fuzzy Boundary Control for Nonlinear Delayed DPSs under Boundary Measurements",

abstract = "For nonlinear delayed distributed parameter systems (DDPSs), this article considers a fuzzy boundary control (FBC) under boundary measurements (BMs). Initially, we accurately describe the nonlinear DDPS through a Takagi-Sugeno (T-S) fuzzy partial differential-difference equation (PDDE). Then, in accordance with the T-S fuzzy PDDE model, an FBC design under BMs ensuring the exponential stability for closed-loop DDPS is subsequently presented by spatial linear matrix inequalities (SLMIs) via using Wirtinger's inequality, Halanay's inequality, and the Lyapunov direct method, which respects the fast-varying and slow-varying delays. Moreover, we formulate SLMIs as LMIs for solving the fuzzy boundary controller design of nonlinear DDPSs under BMs. Finally, the effectiveness of the proposed FBC strategy is presented via simulation examples.",

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author = "Wang, \{Zi Peng\} and Xu Zhang and Wu, \{Huai Ning\} and Tingwen Huang",

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T1 - Fuzzy Boundary Control for Nonlinear Delayed DPSs under Boundary Measurements

AU - Wang, Zi Peng

AU - Zhang, Xu

AU - Wu, Huai Ning

AU - Huang, Tingwen

PY - 2023/3/1

Y1 - 2023/3/1

N2 - For nonlinear delayed distributed parameter systems (DDPSs), this article considers a fuzzy boundary control (FBC) under boundary measurements (BMs). Initially, we accurately describe the nonlinear DDPS through a Takagi-Sugeno (T-S) fuzzy partial differential-difference equation (PDDE). Then, in accordance with the T-S fuzzy PDDE model, an FBC design under BMs ensuring the exponential stability for closed-loop DDPS is subsequently presented by spatial linear matrix inequalities (SLMIs) via using Wirtinger's inequality, Halanay's inequality, and the Lyapunov direct method, which respects the fast-varying and slow-varying delays. Moreover, we formulate SLMIs as LMIs for solving the fuzzy boundary controller design of nonlinear DDPSs under BMs. Finally, the effectiveness of the proposed FBC strategy is presented via simulation examples.

AB - For nonlinear delayed distributed parameter systems (DDPSs), this article considers a fuzzy boundary control (FBC) under boundary measurements (BMs). Initially, we accurately describe the nonlinear DDPS through a Takagi-Sugeno (T-S) fuzzy partial differential-difference equation (PDDE). Then, in accordance with the T-S fuzzy PDDE model, an FBC design under BMs ensuring the exponential stability for closed-loop DDPS is subsequently presented by spatial linear matrix inequalities (SLMIs) via using Wirtinger's inequality, Halanay's inequality, and the Lyapunov direct method, which respects the fast-varying and slow-varying delays. Moreover, we formulate SLMIs as LMIs for solving the fuzzy boundary controller design of nonlinear DDPSs under BMs. Finally, the effectiveness of the proposed FBC strategy is presented via simulation examples.

KW - Boundary measurements (BMs)

KW - delayed distributed parameter systems (DDPSs)

KW - fuzzy boundary control (FBC)

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JO - IEEE Transactions on Cybernetics

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Fuzzy Boundary Control for Nonlinear Delayed DPSs under Boundary Measurements

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Keywords

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