# Optimized Radial Basis Function Neural Network Based Intelligent Control Algorithm of Unmanned Surface Vehicles

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## Abstract

**:**

## 1. Introduction

## 2. RBF Neural Network and Its Genetic Optimization

#### 2.1. RBF Neural Network Approximation Algorithm

#### 2.2. Optimization of the RBF Neural Network based on the Genetic Algorithm

- (1)
- To solve any form of objective function and constraint optimization problem, whether it is linear or nonlinear, discrete or continuous, the genetic algorithm does not require any mathematical model. Depending on its evolutionary nature, the inherent nature of the problem need not be known during the search process.
- (2)
- The ergodicity of evolutionary operators makes genetic algorithms very efficient in globally searching for probabilistic meanings.
- (3)
- For a variety of special problems, genetic algorithms can provide great flexibility to mix and construct domain-independent heuristics, thereby ensuring the effectiveness of the algorithm.

**Step 1:**The N subpopulations are initialized, and the initial network parameters (connection weights, center width, and center value of the Gaussian function) are encoded as genes.

**Step 2:**N subpopulations carry out evolutionary operations independently.

**Step 3:**Performance judgement? If no, go to the next step. If yes, end, and go to the RBF learning step.

- (1)
- Firstly, autonomous learning of the RBF network.
- (2)
- Secondly, absolute error calculation.
- (3)
- Thirdly, parameter updating.
- (4)
- Finally, performance judgement? If Yes, end. If No, go to autonomous learning and error calculation.

**Step 4:**The average fitness of N subpopulations is calculated.

**Step 5:**The selection and cross operations are performed separately.

**Step 6:**Mutation operations are performed separately.

**Step 7:**The new N subpopulations are recalculated and returned to Step 2.

#### 2.2.1. Adaptation Value Correction

_{1}> 1. The effect of this correction is to reduce the influence of genes whose adaptation value is too large, slow down their convergence speed, and expand the search space.

#### 2.2.2. Correction of Mutation Probability

## 3. USV Ideal Sliding Mode Control Based on the RBF Neural Network

#### 3.1. USV Motion Mathematical Model

#### 3.2. Ideal Sliding Mode Control Based on the RBF Neural Network

_{0}.

## 4. Computer Simulation Experiment Results and Analysis

#### 4.1. Verification of Practical Performance Experiments

#### 4.2. Verification of Advanced Performance Experiments

## 5. Analysis and Discussion of Results

#### 5.1. Control Performance of the Intelligent Algorithm Based on an IGA-Optimized RBF Network

#### 5.2. Comparison of USV Navigation Control

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Algorithms | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Average | Average/Median |
---|---|---|---|---|---|---|---|---|---|---|---|

GA | 902 | 922 | 958 | 960 | 976 | 1003 | 1011 | 1022 | 1015 | 974.33 | 0.998 |

IGA | 740 | 775 | 790 | 800 | 842 | 854 | 858 | 861 | 873 | 821.44 | 0.975 |

Experiments | Stabilization Time | Overshoot | Chattering |
---|---|---|---|

A | 65 s | 0 | 0 |

B | 68 s | 0 | 0 |

C | 70 s | 0.8% | 0 |

D | 75 s | 1.0% | 1% |

E | 80 s | 1.2% | 2% |

Control Algorithms | Stabilization Time | Overshoot | Chattering |
---|---|---|---|

Based on RBF Network optimized by IGA | 80 s | 1.2% | Weak |

Based on the Fuzzy Neural Network | 120 s | 1.5% | Little |

Based on the RBF Network | 130 s | 2.0% | Medium |

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**MDPI and ACS Style**

Wang, R.; Li, D.; Miao, K. Optimized Radial Basis Function Neural Network Based Intelligent Control Algorithm of Unmanned Surface Vehicles. *J. Mar. Sci. Eng.* **2020**, *8*, 210.
https://doi.org/10.3390/jmse8030210

**AMA Style**

Wang R, Li D, Miao K. Optimized Radial Basis Function Neural Network Based Intelligent Control Algorithm of Unmanned Surface Vehicles. *Journal of Marine Science and Engineering*. 2020; 8(3):210.
https://doi.org/10.3390/jmse8030210

**Chicago/Turabian Style**

Wang, Renqiang, Donglou Li, and Keyin Miao. 2020. "Optimized Radial Basis Function Neural Network Based Intelligent Control Algorithm of Unmanned Surface Vehicles" *Journal of Marine Science and Engineering* 8, no. 3: 210.
https://doi.org/10.3390/jmse8030210