# Adaptive Fixed-Time Control of Strict-Feedback High-Order Nonlinear Systems

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## Abstract

**:**

## 1. Introduction

- (1)
- The combination of the neural network adaptive control with fixed-time Lyapunov stability theory for high-order nonlinear system control problems.
- (2)
- The design of the fixed-time adaptive law of the error systems for neural networks. The parameters of neural networks are iteratively in fixed time based on the Lyapunov fixed-time stability theorem.
- (3)
- The convergence time set by control parameters and adaptive law gain parameters without initial conditions to ensure the control performance.

## 2. Problem Formation and Preliminaries

**Lemma**

**1.**

**Lemma**

**2.**

**Proof.**

## 3. Main Results

**Theorem**

**1.**

**Proof.**

## 4. Numerical Examples

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**MDPI and ACS Style**

Li, Y.; Zhang, J.; Ye, X.; Chin, C.S.
Adaptive Fixed-Time Control of Strict-Feedback High-Order Nonlinear Systems. *Entropy* **2021**, *23*, 963.
https://doi.org/10.3390/e23080963

**AMA Style**

Li Y, Zhang J, Ye X, Chin CS.
Adaptive Fixed-Time Control of Strict-Feedback High-Order Nonlinear Systems. *Entropy*. 2021; 23(8):963.
https://doi.org/10.3390/e23080963

**Chicago/Turabian Style**

Li, Yang, Jianhua Zhang, Xiaoyun Ye, and Cheng Siong Chin.
2021. "Adaptive Fixed-Time Control of Strict-Feedback High-Order Nonlinear Systems" *Entropy* 23, no. 8: 963.
https://doi.org/10.3390/e23080963