# Prediction Governors for Input-Affine Nonlinear Systems and Application to Automatic Driving Control

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## Abstract

**:**

## 1. Introduction

## 2. Optimal Prediction Governor for Input-Affine Nonlinear Systems

#### 2.1. Problem Formulation

**Problem**

**1.**

#### 2.2. Optimal Prediction Governor

**Theorem**

**1.**

**Proof**

**of Theorem 1.**

- (i)
- Calculate $\left[0\phantom{\rule{3.33333pt}{0ex}}0\phantom{\rule{3.33333pt}{0ex}}{I}_{n}\right]\xi (t+1)$ in the first formula.
- (ii)
- Using the second formula, calculate $\left[0\phantom{\rule{3.33333pt}{0ex}}{I}_{n}\phantom{\rule{3.33333pt}{0ex}}0\right]\xi (t+1)$.
- (iii)
- Using the third formula, calculate $v\left(t\right)$.
- (iv)
- Calculate $\left[{I}_{n}\phantom{\rule{3.33333pt}{0ex}}0\phantom{\rule{3.33333pt}{0ex}}0\right]\xi (t+1)$ in the first formula.

## 3. Application to Automatic Driving Control

#### 3.1. Simulation

#### 3.2. Experiment

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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Item | Specification | |
---|---|---|

Body | Size, weight | 190 × 429 × 150 (mm), 2.2 (kg) |

Minimum turning radius | 500 (mm) | |

maximum speed | 10 (km/h) | |

Motor | Drive: Small DC motor, Steering: Servomotor for robot | |

External sensor | USB camera (640×480 (pix), 30 (fps), 128 (deg)) | |

Inner Sensor | Rotary encoder | |

CPU | Intel Celeron Quad Core 1.83 (GHz) | |

Software | OS | Linux (Ubuntu 14.04) |

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**MDPI and ACS Style**

Minami, Y.; Iwai, Y.
Prediction Governors for Input-Affine Nonlinear Systems and Application to Automatic Driving Control. *Robotics* **2018**, *7*, 16.
https://doi.org/10.3390/robotics7020016

**AMA Style**

Minami Y, Iwai Y.
Prediction Governors for Input-Affine Nonlinear Systems and Application to Automatic Driving Control. *Robotics*. 2018; 7(2):16.
https://doi.org/10.3390/robotics7020016

**Chicago/Turabian Style**

Minami, Yuki, and Yudai Iwai.
2018. "Prediction Governors for Input-Affine Nonlinear Systems and Application to Automatic Driving Control" *Robotics* 7, no. 2: 16.
https://doi.org/10.3390/robotics7020016