# Time-Varying Formation Tracking Control for Unmanned Aerial Vehicles with the Leader’s Unknown Input and Obstacle Avoidance: Theories and Applications

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## Abstract

**:**

## 1. Introduction

## 2. Preliminaries and Problem Description

#### 2.1. Basic Graph Theory

#### 2.2. Problem Description

**Definition**

**1.**

**Assumption**

**1.**

**Assumption**

**2.**

**Assumption**

**3.**

**Lemma**

**2**

**.**Under Assumption 2, there exists a positive matrix $\mathsf{\Gamma}=diag(\gamma )$ generated from $\gamma ={[{\gamma}_{1},{\gamma}_{2},\cdots ,{\gamma}_{N-1}]}^{T}$, where ${\gamma}_{i}$ equals the reciprocal of the ith component of ${L}_{FF}^{-1}\mathbf{1}$, such that ${\widehat{L}}_{FF}=\mathsf{\Gamma}{L}_{FF}+{L}_{FF}^{T}\mathsf{\Gamma}$ is symmetric and positive definite.

**Definition**

**2.**

**Definition**

**3.**

## 3. Theoretical Analysis

**Lemma**

**3**

**.**The distributed observer ${\eta}_{i}$ can realize a fixed-time consensus with the position of the leader under Assumptions 1–2 and the proposed protocol (8) with $\mu >0$ satisfying:

**Theorem**

**1.**

**Proof.**

**Remark**

**1.**

**Remark**

**2.**

## 4. Numerical and Experimental Results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

TVFT | time-varying formation tracking |

UAV | unmanned aerial vehicle |

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**MDPI and ACS Style**

Li, Q.; Hua, Y.; Dong, X.; Yu, J.; Ren, Z.
Time-Varying Formation Tracking Control for Unmanned Aerial Vehicles with the Leader’s Unknown Input and Obstacle Avoidance: Theories and Applications. *Electronics* **2022**, *11*, 2334.
https://doi.org/10.3390/electronics11152334

**AMA Style**

Li Q, Hua Y, Dong X, Yu J, Ren Z.
Time-Varying Formation Tracking Control for Unmanned Aerial Vehicles with the Leader’s Unknown Input and Obstacle Avoidance: Theories and Applications. *Electronics*. 2022; 11(15):2334.
https://doi.org/10.3390/electronics11152334

**Chicago/Turabian Style**

Li, Qing, Yongzhao Hua, Xiwang Dong, Jianglong Yu, and Zhang Ren.
2022. "Time-Varying Formation Tracking Control for Unmanned Aerial Vehicles with the Leader’s Unknown Input and Obstacle Avoidance: Theories and Applications" *Electronics* 11, no. 15: 2334.
https://doi.org/10.3390/electronics11152334