# Output Feedback Control for Spacecraft Attitude System with Practical Predefined-Time Stability Based on Anti-Windup Compensator

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## Abstract

**:**

## 1. Introduction

## 2. Problem Formulation

#### 2.1. Preliminaries

**Lemma**

**1.**

**Lemma**

**2.**

**Lemma**

**3.**

**Lemma**

**4.**

**Lemma**

**5.**

**Lemma**

**6.**

#### 2.2. Rigid Spacecraft Attitude Dynamic Model

**Assumption**

**1.**

**Assumption**

**2.**

**Assumption**

**3.**

#### 2.3. Model Transformation

**Remark**

**1.**

**Remark**

**2.**

**Remark**

**3.**

**ω**of the original system [28]. Hence, the main control objective is to stabilize the converted system (20) within a predefined time despite the mismatched uncertainty ζ. To this end, we employ an adaptive predefined-time back-stepping control strategy.

## 3. Adaptive Predefined-Time Attitude Control

**Remark**

**4.**

**δ**, we just need to show that both

**ζ**and ${\dot{\mathit{\phi}}}_{1}$ are bounded. The boundedness of

**ζ**has been analyzed in Remark 1. Moreover, the denominator of the virtual control ${\mathit{\phi}}_{1}$ in Equation (24) is always positive and nonzero; thus, it is well defined. Its time derivative is also bounded. To be more exact, its time derivative is obtained as follows:

**Theorem**

**1.**

**Proof.**

**Remark**

**5.**

## 4. Simulation Results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**MDPI and ACS Style**

Xuan-Mung, N.; Golestani, M.; Nguyen, H.T.; Nguyen, N.A.; Fekih, A.
Output Feedback Control for Spacecraft Attitude System with Practical Predefined-Time Stability Based on Anti-Windup Compensator. *Mathematics* **2023**, *11*, 2149.
https://doi.org/10.3390/math11092149

**AMA Style**

Xuan-Mung N, Golestani M, Nguyen HT, Nguyen NA, Fekih A.
Output Feedback Control for Spacecraft Attitude System with Practical Predefined-Time Stability Based on Anti-Windup Compensator. *Mathematics*. 2023; 11(9):2149.
https://doi.org/10.3390/math11092149

**Chicago/Turabian Style**

Xuan-Mung, Nguyen, Mehdi Golestani, Huu Tiep Nguyen, Ngoc Anh Nguyen, and Afef Fekih.
2023. "Output Feedback Control for Spacecraft Attitude System with Practical Predefined-Time Stability Based on Anti-Windup Compensator" *Mathematics* 11, no. 9: 2149.
https://doi.org/10.3390/math11092149