# Tracking Control of a Class of Chaotic Systems

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Problem Formation

**Remark**

**1.**

## 3. Main Result

#### 3.1. The Reference Model

**Remark**

**2.**

**Theorem**

**1.**

**Proof.**

#### 3.2. Control Design

**Remark**

**3.**

## 4. Numerical Examples

**Example**

**1.**

**Example**

**2.**

**Example**

**3.**

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Shows that the state ${x}_{1}$ of the system (15) converges to $c\left(t\right)=5$ as $t\to \infty $.

**Figure 2.**Shows the state ${({x}_{2},{x}_{3})}^{T}$ of the system (15) converges to a constant as $t\to \infty $.

**Figure 3.**Shows the state ${x}_{1}$ of the system (22) converges to $c\left(t\right)=sin\left(3t\right)$ as $t\to \infty $.

**Figure 4.**Shows the state ${({x}_{2},{x}_{3})}^{T}$ of the system (22) converges to a constant as $t\to \infty $.

**Figure 5.**Shows the states ${({x}_{1},{x}_{2})}^{T}$ of the system (22) converges to $c\left(t\right)={(3cos\left(t\right),3sin\left(t\right))}^{T}$ as $t\to \infty $.

**Figure 6.**Shows phase portrait of the states ${({x}_{1},{x}_{2})}^{T}$ of the system (29) converges to a circle with radius 3 as $t\to \infty $.

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**MDPI and ACS Style**

Yang, A.; Li, L.; Wang, Z.; Guo, R.
Tracking Control of a Class of Chaotic Systems. *Symmetry* **2019**, *11*, 568.
https://doi.org/10.3390/sym11040568

**AMA Style**

Yang A, Li L, Wang Z, Guo R.
Tracking Control of a Class of Chaotic Systems. *Symmetry*. 2019; 11(4):568.
https://doi.org/10.3390/sym11040568

**Chicago/Turabian Style**

Yang, Anqing, Linshan Li, Zuoxun Wang, and Rongwei Guo.
2019. "Tracking Control of a Class of Chaotic Systems" *Symmetry* 11, no. 4: 568.
https://doi.org/10.3390/sym11040568