# Robust Output Path-Following Control of Marine Surface Vessels with Finite-Time LOS Guidance

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## Abstract

**:**

## 1. Introduction

- The path-following problem is formulated with unknown time-varying sideslip angle, unmeasured system state and system uncertainties, thus, the observation technique is adopted to estimate all these unknown terms.
- A finite-time generalized observer is proposed for sideslip angle estimation, based on which a nonlinear LOS guidance law is proposed, and finite-time convergence of the cross-track error is hence obtained.
- An ESO is adopted for both unknown system state and total disturbance estimation, based on which an output feedback backstepping controller is proposed without angular velocity measurement.

## 2. Preliminaries and System Description

#### 2.1. Preliminaries

**Definition**

**1.**

**Lemma**

**1**

**.**Considering the system in following form

#### 2.2. Kinematics of Path Following

#### 2.3. Yaw Dynamics of Marine Surface Vessels

## 3. Control System Design

#### 3.1. FGO Based Finite-Time LOS Guidance

**Theorem**

**1.**

**Proof.**

**Theorem**

**2.**

**Proof.**

#### 3.2. Output Feedback Controller Based on ADRC

**Assumption**

**A1.**

**Theorem**

**3.**

**Proof.**

## 4. Stability Analysis

**Theorem**

**4.**

**Proof.**

## 5. Numerical Simulations

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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Settling Time | Overshot | |
---|---|---|

Proposed method | 113 s | 0.0089% |

Adaptive LOS | 162 s | 1.3521% |

Integral LOS | 259 s | 31.6269% |

Maximum Error | RMSE | |
---|---|---|

Proposed method | 0.1564 m | 0.0275 m |

Adaptive LOS | 3.1063 m | 1.5261 m |

Integral LOS | 4.5996 m | 1.7025 m |

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## Share and Cite

**MDPI and ACS Style**

Wang, L.; Xu, C.; Cheng, J.
Robust Output Path-Following Control of Marine Surface Vessels with Finite-Time LOS Guidance. *J. Mar. Sci. Eng.* **2020**, *8*, 275.
https://doi.org/10.3390/jmse8040275

**AMA Style**

Wang L, Xu C, Cheng J.
Robust Output Path-Following Control of Marine Surface Vessels with Finite-Time LOS Guidance. *Journal of Marine Science and Engineering*. 2020; 8(4):275.
https://doi.org/10.3390/jmse8040275

**Chicago/Turabian Style**

Wang, Lu, Changkui Xu, and Jianhua Cheng.
2020. "Robust Output Path-Following Control of Marine Surface Vessels with Finite-Time LOS Guidance" *Journal of Marine Science and Engineering* 8, no. 4: 275.
https://doi.org/10.3390/jmse8040275