# Uncertainty Observer-Based Control for a Class of Fractional- Order Non-Linear Systems with Non-Linear Control Inputs

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Main Result

#### Preliminaries

**Definition 1.**

**Definition 2.**

**Lemma 1**

**Lemma 2**

## 3. Uncertainty Estimation Observer and Controller

**Assumption 1.**

**Assumption 2.**

**Assumption 3.**

**Assumption 4.**

**Assumption 5.**

## 4. The Thermoelectric Module and Numerical Results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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New Variable | Numerical Value | New Variable | Numerical Value |
---|---|---|---|

${A}_{1}$ | 0.002733 | ${C}_{6}$ | 0.00227 |

${A}_{2}$ | 0.000564 | ${C}_{7}$ | $3.2930\times {10}^{-8}$ |

${B}_{1}$ | 41.389 | ${D}_{1}$ | 109.8051 |

${B}_{2}$ | 41.38907 | ${D}_{2}$ | 0.001649 |

${B}_{3}$ | 1.3545 | ${D}_{3}$ | 0.012514 |

${B}_{4}$ | 0.003419 | ${D}_{4}$ | 0.012039 |

${C}_{1}$ | 243.79 | ${D}_{5}$ | 0.00497 |

${C}_{2}$ | 0.05489 | ${D}_{6}$ | 0.00453 |

${C}_{3}$ | 0.00392 | ${D}_{7}$ | 5.82857 |

${C}_{4}$ | 0.01242 | $\alpha $ | 0.912634 |

${C}_{5}$ | 0.00314 |

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**MDPI and ACS Style**

Montesinos-García, J.J.; Barahona-Avalos, J.L.; Linares-Flores, J.; Juárez-Abad, J.A.
Uncertainty Observer-Based Control for a Class of Fractional- Order Non-Linear Systems with Non-Linear Control Inputs. *Fractal Fract.* **2023**, *7*, 836.
https://doi.org/10.3390/fractalfract7120836

**AMA Style**

Montesinos-García JJ, Barahona-Avalos JL, Linares-Flores J, Juárez-Abad JA.
Uncertainty Observer-Based Control for a Class of Fractional- Order Non-Linear Systems with Non-Linear Control Inputs. *Fractal and Fractional*. 2023; 7(12):836.
https://doi.org/10.3390/fractalfract7120836

**Chicago/Turabian Style**

Montesinos-García, Juan Javier, Jorge Luis Barahona-Avalos, Jesús Linares-Flores, and José Antonio Juárez-Abad.
2023. "Uncertainty Observer-Based Control for a Class of Fractional- Order Non-Linear Systems with Non-Linear Control Inputs" *Fractal and Fractional* 7, no. 12: 836.
https://doi.org/10.3390/fractalfract7120836