The Finite-Time Stability of a Class of Fractional Order Nonlinear Systems via Dynamic Sliding Mode

2018 ◽  
Author(s):  
Keyong Shao ◽  
Yi Zhang
Keyword(s):  
Nonlinear Systems ◽  
Fractional Order ◽  
Finite Time ◽  
Sliding Mode ◽  
Time Stability ◽  
Finite Time Stability ◽  
Dynamic Sliding Mode

Chattering-Free Finite-Time Stability of a Class of Fractional-Order Nonlinear Systems

2019 ◽  
Author(s):  
Bin Wang ◽  
Yangquan Chen ◽  
Ying Yang
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Finite Time ◽  
Sliding Mode ◽  
Time Stability ◽  
External Disturbances ◽  
Finite Time Stability ◽  
Mode Control ◽  
Chattering Free

Abstract This paper studies the chattering-free finite-time control for a class of fractional-order nonlinear systems. First, a class of fractional-order nonlinear systems with external disturbances is presented. Second, a new finite-time terminal sliding mode control method is proposed for the stability control of a class of fractional-order nonlinear systems by combining the finite-time stability theory and sliding mode control scheme. Third, by designing a controller with a differential form and introducing the arc tangent function, the chattering phenomenon is well suppressed. Additionally, a controller is developed to resist external disturbances. Finally, numerical simulations are implemented to demonstrate the feasibility and validity of the proposed method.

scholarly journals Finite time stability and sliding mode control for uncertain variable fractional order nonlinear systems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jingfei Jiang ◽  
Hongkui Li ◽  
Kun Zhao ◽  
Dengqing Cao ◽  
Juan L. G. Guirao
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Finite Time ◽  
Sliding Mode ◽  
Direct Method ◽  
Uncertain Variable ◽  
Time Stability ◽  
Finite Time Stability ◽  
Mode Control

AbstractThis paper deals with the finite time stability and control for a class of uncertain variable fractional order nonlinear systems. The variable fractional Lyapunov direct method is developed to provide the basis for the stability proof of the system considered. The sliding mode control method is applied for robust control of uncertain variable fractional order systems; furthermore, the chattering phenomenon is avoided. And the finite time stability of the systems under control law is proved based on the proposed stability criterion. Finally, numerical simulations are proposed and the efficiency of the controller is verified.

Neural Adaptive Fault Tolerant Control of Nonlinear Fractional Order Systems Via Terminal Sliding Mode Approach

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Bijan Hashtarkhani ◽  
Mohammad Javad Khosrowjerdi
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Fault Tolerant ◽  
Sliding Mode ◽  
Fault Tolerant Control ◽  
State Feedback Control ◽  
Time Stability ◽  
Terminal Sliding Mode ◽  
Finite Time Stability ◽  
Output Tracking

This article proposes an adaptive neural output tracking control scheme for a class of nonlinear fractional order (FO) systems in the presence of unknown actuator faults. By means of backstepping terminal sliding mode (SM) control technique, an adaptive fractional state-feedback control law is extracted to achieve finite time stability along with output tracking for an uncertain faulty FO system. The unknown nonlinear terms are approximated by radial-basis function neural network (RBFNN) with unknown approximation error upper bound. Using convergence in finite time and fractional Lyapunov stability theorems, the finite time stability and tracking achievement are proved. Finally, the proposed fault tolerant control (FTC) approach is validated with numerical simulations on two fractional models including fractional Genesio–Tesi and fractional Duffing's oscillator systems.

scholarly journals Finite-time stability of linear stochastic fractional-order systems with time delay

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Lassaad Mchiri ◽  
Abdellatif Ben Makhlouf ◽  
Dumitru Baleanu ◽  
Mohamed Rhaima
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Finite Time ◽  
Stochastic Analysis ◽  
Fractional Order Systems ◽  
Time Stability ◽  
Finite Time Stability ◽  
Analysis Techniques ◽  
Generalized Gronwall Inequality ◽  
Stability Of The Solution

AbstractThis paper focuses on the finite-time stability of linear stochastic fractional-order systems with time delay for $\alpha \in (\frac{1}{2},1)$ α ∈ ( 1 2 , 1 ) . Under the generalized Gronwall inequality and stochastic analysis techniques, the finite-time stability of the solution for linear stochastic fractional-order systems with time delay is investigated. We give two illustrative examples to show the interest of the main results.

scholarly journals FTS and FTB of Conformable Fractional Order Linear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Abdellatif Ben Makhlouf ◽  
Omar Naifar ◽  
Mohamed Ali Hammami ◽  
Bao-wei Wu
Keyword(s):  
Fractional Derivative ◽  
Linear Systems ◽  
Fractional Order ◽  
Finite Time ◽  
Conformable Fractional Derivative ◽  
Time Stability ◽  
Order Linear ◽  
Finite Time Stability ◽  
Finite Time Boundedness

In this paper, an extension of some existing results related to finite-time stability (FTS) and finite-time boundedness (FTB) into the conformable fractional derivative is presented. Illustrative example is presented at the end of the paper to show the effectiveness of the proposed result.

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