Fuzzy Intermittent Control for Nonlinear Coupled Delayed PDE-ODE Systems

Zi-Peng Wang; Hua-Ran Su; Xi-Dong Shi; Junfei Qiao; Huai-Ning Wu; Han-Xiong Li

doi:10.1109/TCYB.2025.3597770

Fuzzy Intermittent Control for Nonlinear Coupled Delayed PDE-ODE Systems

Zi-Peng Wang^*, Hua-Ran Su, Xi-Dong Shi, Junfei Qiao, Huai-Ning Wu, Han-Xiong Li

^*Corresponding author for this work

Department of Systems Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

4 Citations (Scopus)

Abstract

In this work, we introduce a fuzzy intermittent control method for nonlinear coupled delayed partial differential equation-ordinary differential equation (PDE-ODE) systems based on spatially averaged measurements (SAMs). First, the nonlinear coupled delayed PDE-ODE systems are accurately modeled by adopting the Takagi-Sugeno (T-S) fuzzy PDE-ODE model. Then, based on the T-S fuzzy PDE-ODE model, a switching lyapunov functional (LF) is given, and fuzzy intermittent controllers are designed to ensure the exponential stability of the closed-loop fuzzy delayed coupled systems. Sufficient conditions for the exponential stability of the system are expressed through by a set of space-dependent linear matrix inequalities (SDLMIs). Finally, the simulation results are used to verify the effectiveness of the proposed approach for controlling hypersonic rocket car (HRC).

© 2025 IEEE. All rights reserved, including rights for text and data mining, and training of artificial intelligence and similar technologies. Personal use is permitted, but republication/redistribution requires IEEE permission.

Original language	English
Pages (from-to)	5766-5779
Number of pages	14
Journal	IEEE Transactions on Cybernetics
Volume	55
Issue number	12
Online published	28 Aug 2025
DOIs	https://doi.org/10.1109/TCYB.2025.3597770
Publication status	Published - Dec 2025

Funding

This work was supported in part by the National Key Research and Development Program of China under Grant 2023YFB3307300 and Grant 2021ZD0112300; in part by the National Natural Science Foundations of China under Grant 62203326 and Grant 62473021; in part by the China Postdoctoral Science Foundation under Grant 2022M720322; and in part by the Beijing Postdoctoral Research Foundation.

Research Keywords

Control systems
Mathematical models
Stability analysis
Delays
Control theory
Rockets
Linear matrix inequalities
Time-varying systems
Technological innovation
Switches
Fuzzy intermittent control
HRC
nonlinear coupled delayed PDE-ODE systems
SDLMIs
SAMs

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title = "Fuzzy Intermittent Control for Nonlinear Coupled Delayed PDE-ODE Systems",

abstract = "In this work, we introduce a fuzzy intermittent control method for nonlinear coupled delayed partial differential equation-ordinary differential equation (PDE-ODE) systems based on spatially averaged measurements (SAMs). First, the nonlinear coupled delayed PDE-ODE systems are accurately modeled by adopting the Takagi-Sugeno (T-S) fuzzy PDE-ODE model. Then, based on the T-S fuzzy PDE-ODE model, a switching lyapunov functional (LF) is given, and fuzzy intermittent controllers are designed to ensure the exponential stability of the closed-loop fuzzy delayed coupled systems. Sufficient conditions for the exponential stability of the system are expressed through by a set of space-dependent linear matrix inequalities (SDLMIs). Finally, the simulation results are used to verify the effectiveness of the proposed approach for controlling hypersonic rocket car (HRC).{\textcopyright} 2025 IEEE. All rights reserved, including rights for text and data mining, and training of artificial intelligence and similar technologies. Personal use is permitted, but republication/redistribution requires IEEE permission.",

keywords = "Control systems, Mathematical models, Stability analysis, Delays, Control theory, Rockets, Linear matrix inequalities, Time-varying systems, Technological innovation, Switches, Fuzzy intermittent control, HRC, nonlinear coupled delayed PDE-ODE systems, SDLMIs, SAMs",

author = "Zi-Peng Wang and Hua-Ran Su and Xi-Dong Shi and Junfei Qiao and Huai-Ning Wu and Han-Xiong Li",

year = "2025",

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doi = "10.1109/TCYB.2025.3597770",

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T1 - Fuzzy Intermittent Control for Nonlinear Coupled Delayed PDE-ODE Systems

AU - Wang, Zi-Peng

AU - Su, Hua-Ran

AU - Shi, Xi-Dong

AU - Qiao, Junfei

AU - Wu, Huai-Ning

AU - Li, Han-Xiong

PY - 2025/12

Y1 - 2025/12

N2 - In this work, we introduce a fuzzy intermittent control method for nonlinear coupled delayed partial differential equation-ordinary differential equation (PDE-ODE) systems based on spatially averaged measurements (SAMs). First, the nonlinear coupled delayed PDE-ODE systems are accurately modeled by adopting the Takagi-Sugeno (T-S) fuzzy PDE-ODE model. Then, based on the T-S fuzzy PDE-ODE model, a switching lyapunov functional (LF) is given, and fuzzy intermittent controllers are designed to ensure the exponential stability of the closed-loop fuzzy delayed coupled systems. Sufficient conditions for the exponential stability of the system are expressed through by a set of space-dependent linear matrix inequalities (SDLMIs). Finally, the simulation results are used to verify the effectiveness of the proposed approach for controlling hypersonic rocket car (HRC).© 2025 IEEE. All rights reserved, including rights for text and data mining, and training of artificial intelligence and similar technologies. Personal use is permitted, but republication/redistribution requires IEEE permission.

AB - In this work, we introduce a fuzzy intermittent control method for nonlinear coupled delayed partial differential equation-ordinary differential equation (PDE-ODE) systems based on spatially averaged measurements (SAMs). First, the nonlinear coupled delayed PDE-ODE systems are accurately modeled by adopting the Takagi-Sugeno (T-S) fuzzy PDE-ODE model. Then, based on the T-S fuzzy PDE-ODE model, a switching lyapunov functional (LF) is given, and fuzzy intermittent controllers are designed to ensure the exponential stability of the closed-loop fuzzy delayed coupled systems. Sufficient conditions for the exponential stability of the system are expressed through by a set of space-dependent linear matrix inequalities (SDLMIs). Finally, the simulation results are used to verify the effectiveness of the proposed approach for controlling hypersonic rocket car (HRC).© 2025 IEEE. All rights reserved, including rights for text and data mining, and training of artificial intelligence and similar technologies. Personal use is permitted, but republication/redistribution requires IEEE permission.

KW - Control systems

KW - Mathematical models

KW - Stability analysis

KW - Delays

KW - Control theory

KW - Rockets

KW - Linear matrix inequalities

KW - Time-varying systems

KW - Technological innovation

KW - Switches

KW - Fuzzy intermittent control

KW - HRC

KW - nonlinear coupled delayed PDE-ODE systems

KW - SDLMIs

KW - SAMs

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U2 - 10.1109/TCYB.2025.3597770

DO - 10.1109/TCYB.2025.3597770

M3 - RGC 21 - Publication in refereed journal

SN - 2168-2267

VL - 55

SP - 5766

EP - 5779

JO - IEEE Transactions on Cybernetics

JF - IEEE Transactions on Cybernetics

IS - 12

ER -

Fuzzy Intermittent Control for Nonlinear Coupled Delayed PDE-ODE Systems

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