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Anti-disturbance depth control based on the robust \(L_{1}\) filter for under-actuated AUV with switched linear parameter varying dynamics

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Abstract

To improve the anti-disturbance stability of the autonomous underwater vehicles (AUVs) under bounded disturbances in amplitude, we develop a robust controller based on the estimated signals generated by the filter. The AUV studied has the characteristics of time-varying delay, under-actuated, and switched linear parameter varying (LPV) dynamics. Both the filter and the control strategies, we proposed are based on the robust \(L_{1}\) performance criterion, which is suitable for the amplitude-bounded disturbances in the ocean environment. In the filter and controller design, the corresponding Lyapunov–Krasovskii functional is established to verify the stability of the systems. As there exist couplings between the designed functional and the system parameter matrices, slack matrices are constructed for decouplings after validating the stability of the under-actuated AUV filtering error system and closed-loop control system. The filter and the controller are obtained in the form of parameter linear matrix inequalities (PLMIs), whose solution is infinite-dimensional matrix inequalities. The approximate basis function and gridding technique are applied to transform the filter and the controller into that of finite dimensional LMIs. The simulation has verified the effectiveness of the robust \(L_{1}\) filter and anti-disturbance depth robust \(L_{1}\) controller.

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Acknowledgements

This work was supported by Joint Fund of National Natural Science Foundation of China and Zhejiang Province under Grant U1809211, and the 2020 Research Program of Sanya Yazhou Bay Science and Technology City, Grant No. SKJC-2020-01-014.

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Authors and Affiliations

  1. Ocean College, Zhejiang University, 1 Zheda Road, Zhoushan, 316000, People’s Republic of China

    Peng Bo, Xingbin Tu, Yan Wei & Fengzhong Qu

  2. Hainan Institute of Zhejiang University, Sanya, People’s Republic of China

    Peng Bo & Fengzhong Qu

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  1. Peng Bo
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  2. Xingbin Tu
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  3. Yan Wei
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  4. Fengzhong Qu
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Correspondence to Fengzhong Qu.

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Bo, P., Tu, X., Wei, Y. et al. Anti-disturbance depth control based on the robust \(L_{1}\) filter for under-actuated AUV with switched linear parameter varying dynamics. J Mar Sci Technol 28, 179–194 (2023). https://doi.org/10.1007/s00773-022-00909-2

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  • DOI: https://doi.org/10.1007/s00773-022-00909-2

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