An improved sampled-data control for a nonlinear dynamic positioning ship with Takagi-Sugeno fuzzy model

Minjie Zheng; Yulai Su; Guoquan Chen; Minjie Zheng; Yulai Su; Guoquan Chen

doi:10.3934/mbe.2024265

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 5: 6019-6041. doi: 10.3934/mbe.2024265

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Theory article

An improved sampled-data control for a nonlinear dynamic positioning ship with Takagi-Sugeno fuzzy model

Navigation College, Jimei University, Xiamen 361021, China

Received: 08 January 2024 Revised: 19 March 2024 Accepted: 08 May 2024 Published: 20 May 2024

This article considered the sampled-data control issue for a dynamic positioning ship (DPS) with the Takagi-Sugeno (T-S) fuzzy model. By introducing new useful terms such as second-order term of time, an improved Lyapunov-Krasovskii function (LKF) was constructed. Additionally, the reciprocally convex method is introduced to bound the derivative of LKF. According to the constructed LKF, the sampling information during the whole sampling period was fully utilized, and less conservatism was obtained. Then, the stability condition, robust performance, mode uncertainty and sampled-data controller design were analyzed by means of the linear matrix inequality (LMI). Finally, an example was given to demonstrate the effectiveness of the proposed method.
- dynamic positioning ship,
- sampled-data control,
- Lyapunov-Krasovskii functional,
- T-S fuzzy model
Citation: Minjie Zheng, Yulai Su, Guoquan Chen. An improved sampled-data control for a nonlinear dynamic positioning ship with Takagi-Sugeno fuzzy model[J]. Mathematical Biosciences and Engineering, 2024, 21(5): 6019-6041. doi: 10.3934/mbe.2024265

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Abstract

This article considered the sampled-data control issue for a dynamic positioning ship (DPS) with the Takagi-Sugeno (T-S) fuzzy model. By introducing new useful terms such as second-order term of time, an improved Lyapunov-Krasovskii function (LKF) was constructed. Additionally, the reciprocally convex method is introduced to bound the derivative of LKF. According to the constructed LKF, the sampling information during the whole sampling period was fully utilized, and less conservatism was obtained. Then, the stability condition, robust performance, mode uncertainty and sampled-data controller design were analyzed by means of the linear matrix inequality (LMI). Finally, an example was given to demonstrate the effectiveness of the proposed method.

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