A novel condition for fixed-time stability and its application in controller design for robust fixed-time chaos stabilization against Hölder continuous uncertainties

2020 ◽  
Author(s):  
Alireza Khanzadeh ◽  
Mahdi Pourgholi ◽  
Elham Amini Boroujeni
Keyword(s):  
Controller Design ◽  
Fixed Time ◽  
Time Stability ◽  
Hölder Continuous ◽  
Chaos Stabilization

Smooth adaptive fixed time convergent controller design for BTT missiles with uncertainties

2019 ◽  
Vol 124 (1273) ◽  
pp. 323-345
Author(s):  
Y. Yun ◽  
S. Tang ◽  
J. Guo ◽  
Y. Yun
Keyword(s):  
Control Algorithm ◽  
Performance Metrics ◽  
Controller Design ◽  
Sliding Mode ◽  
Fixed Time ◽  
Convergence Time ◽  
Control Input ◽  
Time Stability ◽  
Terminal Sliding Mode ◽  
Satisfactory Performance

ABSTRACTA smooth adaptive sliding-mode-based controller is developed for BTT missiles considering nonlinear couplings and aerodynamic uncertainties, wherein fixed-time stability theory is synthesised into sliding-mode control algorithm, such that control variables follow the desired command within fixed-bounded convergence time. Unlike other terminal sliding-mode-related works, the bound of settling time is independent of initial states, indicating that performance metrics, for instance the convergence rate, can be evaluated in advance. The control input is designed to be intrinsically smooth, based on adaptive estimations, and therefore the problem of singularity and chattering is effectively eliminated. Simulation results demonstrate the satisfactory performance and validate the effectiveness of the designed approach.

scholarly journals Fixed-Time Stability Analysis of Permanent Magnet Synchronous Motors with Novel Adaptive Control

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Maoxing Liu ◽  
Jie Wu ◽  
Yong-zheng Sun
Keyword(s):  
Stability Analysis ◽  
Permanent Magnet ◽  
Initial Conditions ◽  
Lyapunov Stability Theory ◽  
Fixed Time ◽  
Stability Control ◽  
Time Stability ◽  
Permanent Magnet Synchronous Motors ◽  
Synchronous Motors ◽  
Comparison Results

We firstly investigate the fixed-time stability analysis of uncertain permanent magnet synchronous motors with novel control. Compared with finite-time stability where the convergence rate relies on the initial permanent magnet synchronous motors state, the settling time of fixed-time stability can be adjusted to desired values regardless of initial conditions. Novel adaptive stability control strategy for the permanent magnet synchronous motors is proposed, with which we can stabilize permanent magnet synchronous motors within fixed time based on the Lyapunov stability theory. Finally, some simulation and comparison results are given to illustrate the validity of the theoretical results.

Fixed time synchronization of a class of chaotic systems based via the saturation control

2021 ◽  
Vol 67 (4 Jul-Aug) ◽  
pp. 041401
Author(s):  
Jiaojiao Fu ◽  
Runzi Luo ◽  
Meichun Huang ◽  
Haipeng Su
Keyword(s):  
Upper Bound ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Fixed Time ◽  
Stability Theorem ◽  
Backstepping Method ◽  
Time Stability ◽  
Saturation Control ◽  
New Chaotic System ◽  
Upper Bound Estimate

In this paper, we discuss the fixed time synchronization of a class of chaotic systems based on the backstepping control with disturbances. A new and important fixed time stability theorem is presented. The upper bound estimate formulas of the settling time are also given which are different from the existing results in the literature. Based on the new fixed time stability theorem, a novel saturation controller for the fixed time synchronization a class of chaotic systems is proposed via the backstepping method. Finally, the new chaotic system is taken as an example to illustrate the applicability of the obtained theory.

A new fixed-time stability theorem and its application to the fixed-time synchronization of neural networks

2020 ◽  
Vol 123 ◽  
pp. 412-419 ◽  
Author(s):  
Chuan Chen ◽  
Lixiang Li ◽  
Haipeng Peng ◽  
Yixian Yang ◽  
Ling Mi ◽  
...  
Keyword(s):  
Neural Networks ◽  
Time Synchronization ◽  
Fixed Time ◽  
Stability Theorem ◽  
Time Stability
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