# Artificial Intelligence-Enhanced UUV Actuator Control

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## Abstract

**:**

^{®}, where the motor process is discretized at multiple step sizes, which is inversely proportional to the computation rate. Performance is compared to canonical benchmarks that are evaluated by the error mean and standard deviation. With a large step size, discrete deterministic artificial intelligence shows a larger error mean than the model-following self-turning regulator approach (the selected benchmark). However, the performance improves with a decreasing step size. The error mean is close to the continuous deterministic artificial intelligence when the step size is reduced to 0.2 s, which means that the computation rate and the sampling period restrict discrete deterministic artificial intelligence. In that case, continuous deterministic artificial intelligence is the most feasible and reliable selection for future applications on unmanned underwater vehicles, since it is superior to all the approaches investigated at multiple computation rates.

## 1. Introduction

#### 1.1. Motivation

#### 1.2. Literature Review

The proposed method is based on feedforward self-awareness using process dynamics.

Feedforward self-awareness using process dynamics is foundational for the proposed method.

#### 1.3. Research Gap and Authors Contribution

**Main Conclusion of the study**

- Recommendation of key threshold discretization and computational speed to duplicate the results of the original prequel [3].
- Validation of the first sequel’s [14] identification of paramountcy of discretization and computational speed.
- Validation of the second sequel’s [13] identification of deterministic artificial intelligence performance and recommended selection of algorithms.

#### 1.4. Organization

## 2. Materials and Methods

#### 2.1. Truth Model for Motor Dynamics

^{®}function provided in Appendix A to perform the discretization, a time step of 0.5 s was used as the initial continuous-time process. $U$(z) and $Y\left(z\right)$ represent the control signal and output in discrete-time using the z-transform. The final form of the difference equation is written as Equation (3), where proximal variables and nomenclature and defined in periodic tables (e.g., Table 1 in this instance).

#### 2.2. Model-Following Self Tuner

#### 2.3. Deterministic Artificial Intelligence

## 3. Results

#### 3.1. Model-Following Self-Tuner Control vs. Deterministic Artificial Intelligence

#### 3.2. Discrete Deterministic Artificial Intelligence vs. Continuous Deterministic Artificial Intelligence

^{®}obtains the results of Section 3. The code is included in Appendix A to help with replications or further constructions based on this article.

## 4. Discussion

#### 4.1. Concluding Remarks

#### 4.2. Recommended Future Research

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

^{®}.

#### Appendix A.1. Discrete Deterministic Artificial Intelligence

#### Appendix A.2. Continuous Deterministic Artificial Intelligence

#### Appendix A.3. All Deterministic Artificial Intelligence

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**Figure 4.**The output signal for the control approaches with a 0.5 s step size. The black line represents the command signal. (

**a**) Output signal obtained from discrete deterministic artificial intelligence approach. (

**b**) Output signal generated from continuous deterministic artificial intelligence approach.

**Figure 5.**The output signal for the deterministic artificial intelligence approaches with a 0.5 s step size. The black line represents the command signal. (

**a**) Output signal obtained from discrete deterministic artificial intelligence approach. (

**b**) Output signal generated from continuous deterministic artificial intelligence approach.

Variable/Acronym | Definition | Variable/Acronym | Definition |
---|---|---|---|

$G$ | Transfer function | $s$ | Differential variable |

$Y$ | Output | $z$ | Difference variable |

$U$ | Input | $t$ | Discrete time variable |

^{1}Such tables are offered throughout the manuscript to aid readability.

Variable/Acronym | Definition | Variable/Acronym | Definition |
---|---|---|---|

${u}^{*}$ | Control input | ${\Phi}_{d}$ | Regressor matrix |

${y}_{d}$ | Desired output | $\widehat{\theta}$ | Parameter vector |

${\widehat{a}}_{1},{\widehat{a}}_{2},{\widehat{a}}_{3},{\widehat{b}}_{1}$ | Estimates | ${a}_{1},{a}_{2},{a}_{3},{b}_{1}$ | True values |

${k}_{p}$ | Proportional gain | ${k}_{d}$ | Difference gain |

$A$ | Coefficients of $U\left(z\right)$ | $B$ | Coefficients of $Y\left(z\right)$ |

^{1}Such tables are offered throughout the manuscript to aid readability.

**Table 3.**Error distribution of comparison between model-following control (MF) and deterministic artificial intelligence with different step sizes.

Method | Step Size (s) | Error Mean | Error Standard Deviation |
---|---|---|---|

Deterministic artificial intelligence | 0.60 | 6.3918 | 4.8100 |

Model-following | 0.60 | 0.0264 | 0.0973 |

Deterministic artificial intelligence | 0.50 | 0.0956 | 0.1632 |

Model-following | 0.50 | 0.0277 | 0.0917 |

Deterministic artificial intelligence | 0.27 | 0.0175 | 0.0545 |

Model-following | 0.27 | 0.0471 | 0.1745 |

Deterministic artificial intelligence | 0.20 | 0.0114 | 0.0487 |

Model-following | 0.20 | 0.0608 | 0.2446 |

**Table 4.**Error distribution of comparison between discrete deterministic artificial intelligence and continuous deterministic artificial intelligence with different step sizes

^{1}.

Deterministic Artificial Intelligence Type | Step Size (s) | Error Mean | Error Standard Deviation |
---|---|---|---|

Discrete | 0.50 | 0.0956 | 0.1632 |

Continuous | 0.50 | 0.0223 | 0.1654 |

Discrete | 0.20 | 0.0114 | 0.0487 |

Continuous | 0.20 | 0.0122 | 0.1401 |

^{1}Integration solver step size matched to discretization interval.

Method | Step Size (s) | Error Mean | Error Standard Deviation |
---|---|---|---|

DAI | 0.60 | 6586% | 2847% |

MF | 0.60 | −72% | −40% |

DAI | 0.50 | 0% | 0% |

MF | 0.50 | −71% | −44% |

DAI | 0.27 | −82% | −67% |

MF | 0.27 | −51% | 7% |

DAI | 0.20 | −88% | −70% |

MF | 0.20 | −36% | 50% |

^{1}Model-following (MF) control and deterministic artificial intelligence (DAI).

**Table 6.**Performance improvement for discrete and continuous deterministic artificial intelligence with different step sizes.

Deterministic Artificial Intelligence Type | Step Size (s) | Error Mean | Error Standard Deviation |
---|---|---|---|

Discrete | 0.50 | 0% | 0% |

Continuous | 0.50 | −77% | 1% |

Discrete | 0.20 | −88% | −70% |

Continuous | 0.20 | −87% | −14% |

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**MDPI and ACS Style**

Wang, Z.; Sands, T. Artificial Intelligence-Enhanced UUV Actuator Control. *AI* **2023**, *4*, 270-288.
https://doi.org/10.3390/ai4010012

**AMA Style**

Wang Z, Sands T. Artificial Intelligence-Enhanced UUV Actuator Control. *AI*. 2023; 4(1):270-288.
https://doi.org/10.3390/ai4010012

**Chicago/Turabian Style**

Wang, Zhiyu, and Timothy Sands. 2023. "Artificial Intelligence-Enhanced UUV Actuator Control" *AI* 4, no. 1: 270-288.
https://doi.org/10.3390/ai4010012