Adaptive smooth sampled-data control for synchronization of T–S fuzzy reaction-diffusion neural networks with actuator saturation

Yuchen Niu; Kaibo Shi; Xiao Cai; Shiping Wen; Yuchen Niu; Kaibo Shi; Xiao Cai; Shiping Wen

doi:10.3934/math.2025054

AIMS Mathematics

2025, Volume 10, Issue 1: 1142-1161. doi: 10.3934/math.2025054

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Research article

Adaptive smooth sampled-data control for synchronization of T–S fuzzy reaction-diffusion neural networks with actuator saturation

1.
College of Electrical Engineering, Sichuan University, Chengdu, Sichuan 610065, China
2.
School of Electronic Information and Electrical Engineering, Chengdu University, Chengdu, Sichuan 610106, China
3.
Cyberspace Institute of Advanced Technology, Guangzhou University, Guangzhou 510006, China
4.
Faculty of Engineering and Information Technology, Australian AI Institute, University of Technology Sydney, Ultimo, NSW 2007, Australia

Received: 20 November 2024 Revised: 03 January 2025 Accepted: 08 January 2025 Published: 20 January 2025
MSC : 35B35, 93C42, 93C43, 96D21

This paper addresses the synchronization issue in T–S fuzzy reaction–diffusion neural networks (TFRNNs) with time-varying delays and actuator saturation. First, an adaptive smooth sampled-data (ASSD) controller is proposed to optimize communication resources. In the ASSD controller, the dynamic forgetting factor is employed to process historical data smoothly, thereby preventing data distortion due to unexpected events. Second, the Lyapunov–Krasovskii functional (LKF), which captures more information about the system, is introduced, and it can provide greater flexibility than the fixed-matrix LKF. Meanwhile, by employing the semi-looped-functional method, the constraint for negative determination of the sum of its derivatives is removed, which enhances the feasibility of expanding the solution. Consequently, a novel criterion and the corresponding algorithm are established to obtain the larger maximum allowable sampling interval (MASI). Finally, simulations demonstrate the effectiveness and superiority of the proposed theoretical results.
- T–S fuzzy reaction–diffusion neural networks,
- sampled-data control,
- synchronization,
- Lyapunov–Krasovskii functional
Citation: Yuchen Niu, Kaibo Shi, Xiao Cai, Shiping Wen. Adaptive smooth sampled-data control for synchronization of T–S fuzzy reaction-diffusion neural networks with actuator saturation[J]. AIMS Mathematics, 2025, 10(1): 1142-1161. doi: 10.3934/math.2025054

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Abstract

This paper addresses the synchronization issue in T–S fuzzy reaction–diffusion neural networks (TFRNNs) with time-varying delays and actuator saturation. First, an adaptive smooth sampled-data (ASSD) controller is proposed to optimize communication resources. In the ASSD controller, the dynamic forgetting factor is employed to process historical data smoothly, thereby preventing data distortion due to unexpected events. Second, the Lyapunov–Krasovskii functional (LKF), which captures more information about the system, is introduced, and it can provide greater flexibility than the fixed-matrix LKF. Meanwhile, by employing the semi-looped-functional method, the constraint for negative determination of the sum of its derivatives is removed, which enhances the feasibility of expanding the solution. Consequently, a novel criterion and the corresponding algorithm are established to obtain the larger maximum allowable sampling interval (MASI). Finally, simulations demonstrate the effectiveness and superiority of the proposed theoretical results.

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