Robust fuzzy dynamic surface formation control for underactuated ships using MLP and LFG

Abstract

This note deals with the leader-following formation problem for multiple underactuated ships in the presence of structure uncertainties and the time-varying parameterized disturbances. Following this ideology, a novel robust fuzzy dynamic surface formation control algorithm is proposed by fusing of the dynamic surface control (DSC), minimal learning parameter (MLP) and low frequency gain-learning (LFG). In the control algorithm, the intermediate virtual control laws do not appear in the finally actual control effort, and only two fuzzy type approximators are introduced to compensate the model uncertainties and the external disturbances, which can effectively overcome the constraints of ‘explosion of complexity’ and ‘curse of dimensionality’ in the traditional approximation-based algorithm. Unlike the current DSC technique, no filter errors are required to be stabilized in the Lyapunov function by virtue of the filter compensation signal, which could optimize the calculation of stabilization analysis. Furthermore, benefiting from the LFG technique, the robustness and applicability of the proposed control algorithm can be improved. Based on the Lyapunov theory analysis, all signals of the closed-loop control system can be guaranteed to be semi-global uniformly ultimately bounded (SGUUB). Finally, the simulated experiment is provided to verify the effectiveness and superiority of the proposed control scheme.

Keywords:

• Underactuated ship
• formation control
• minimal learning parameter
• dynamic surface control
• low-frequency gain-learning

Acknowledgments

The authors would like to express our gratitude to the Editor-in-Chief, the Associate Editor, as well as the anonymous reviewers for the time and effort that had been spent in processing our manuscript.

Data availability statement

The data that support the findings of this study are available from the corresponding author, Guoqing Zhang, upon reasonable request.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This paper is partially supported by the National Natural Science Foundation of China [grant numbers 51909018, 51679024, 52171291], the Natural Science Foundation of Liaoning Province [grant numbers 20170520189, 20180520039], the Science and Technology Innovation Foundation of Dalian City [grant number 2019J12GX026], the Fundamental Research Funds for the Central Universities in China [grant number 3132020124].