Double-quantized-based $ H_{\infty} $ tracking control of T-S fuzzy semi-Markovian jump systems with adaptive event-triggered

Yuxin Lou; Mengzhuo Luo; Jun Cheng; Xin Wang; Kaibo Shi; Yuxin Lou; Mengzhuo Luo; Jun Cheng; Xin Wang; Kaibo Shi

doi:10.3934/math.2023351

AIMS Mathematics

2023, Volume 8, Issue 3: 6942-6969. doi: 10.3934/math.2023351

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Research article

Double-quantized-based $ H_{\infty} $ tracking control of T-S fuzzy semi-Markovian jump systems with adaptive event-triggered

1.
College of Science, Guilin University of Technology, Guilin, Guangxi 541004, China
2.
College of Mathematics and Statistics, Guangxi Normal University, Guilin, Guangxi 541006, China
3.
School of Cyber Science and Engineering, Sichuan University, Chengdu, Sichuan 610065, China
4.
School of Information Science and Engineering, Chengdu University, Chengdu, Sichuan 610106, China

Received: 08 November 2022 Revised: 03 December 2022 Accepted: 19 December 2022 Published: 10 January 2023
MSC : 93C15, 93B36

This paper investigates the issue of asynchronous $ H_{\infty} $ tracking control for nonlinear semi-Markovian jump systems (SMJSs) based on the T-S fuzzy model. Firstly, in order to improve the performance of network control systems (NCSs) and the efficiency of data transmission, this paper adopts a double quantization strategy which quantifies the input and output of the controllers. Secondly, for the purpose of reducing the burden of network communication, an adaptive event-triggered mechanism (AETM) is adopted. Thirdly, due to the influence of network-induce delay, the system mode information can not be transmitted to the controller synchronously, thus, a continuous-time hidden Markov model (HMM) is established to describe the asynchronous phenomenon between the system and the controller. Additionally, with the help of some improved Lyapunov-Krasovski (L-K) functions with fuzzy basis, some sufficient criteria are derived to co-guarantee the state stability and the $ H_{\infty} $ performance for the closed-loop tracking control system. Finally, a numerical example and a practical example are given to verify the effectiveness of designed mentality.
- fuzzy semi-Markovian jump systems,
- asynchronous $ H_{\infty} $ control,
- adaptive event-triggered mechanism,
- double quantization,
- tracking control
Citation: Yuxin Lou, Mengzhuo Luo, Jun Cheng, Xin Wang, Kaibo Shi. Double-quantized-based $ H_{\infty} $ tracking control of T-S fuzzy semi-Markovian jump systems with adaptive event-triggered[J]. AIMS Mathematics, 2023, 8(3): 6942-6969. doi: 10.3934/math.2023351

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Abstract

This paper investigates the issue of asynchronous $ H_{\infty} $ tracking control for nonlinear semi-Markovian jump systems (SMJSs) based on the T-S fuzzy model. Firstly, in order to improve the performance of network control systems (NCSs) and the efficiency of data transmission, this paper adopts a double quantization strategy which quantifies the input and output of the controllers. Secondly, for the purpose of reducing the burden of network communication, an adaptive event-triggered mechanism (AETM) is adopted. Thirdly, due to the influence of network-induce delay, the system mode information can not be transmitted to the controller synchronously, thus, a continuous-time hidden Markov model (HMM) is established to describe the asynchronous phenomenon between the system and the controller. Additionally, with the help of some improved Lyapunov-Krasovski (L-K) functions with fuzzy basis, some sufficient criteria are derived to co-guarantee the state stability and the $ H_{\infty} $ performance for the closed-loop tracking control system. Finally, a numerical example and a practical example are given to verify the effectiveness of designed mentality.

References

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