Partial practical stability for fractional‐order nonlinear systems

2022 ◽  
Author(s):  
Abdellatif Ben Makhlouf
Keyword(s):  
Nonlinear Systems ◽  
Fractional Order ◽  
Practical Stability

scholarly journals Observer-based adaptive neural network backstepping sliding mode control for switched fractional order uncertain nonlinear systems with unmeasured states

2021 ◽  
pp. 002029402110211
Author(s):  
Tao Chen ◽  
Damin Cao ◽  
Jiaxin Yuan ◽  
Hui Yang
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Tracking Error ◽  
Adaptive Neural Network ◽  
Dynamic Surface ◽  
Mode Control ◽  
The Stability

This paper proposes an observer-based adaptive neural network backstepping sliding mode controller to ensure the stability of switched fractional order strict-feedback nonlinear systems in the presence of arbitrary switchings and unmeasured states. To avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously, the fractional order dynamic surface control (DSC) technology is introduced into the controller. An observer is used for states estimation of the fractional order systems. The sliding mode control technology is introduced to enhance robustness. The unknown nonlinear functions and uncertain disturbances are approximated by the radial basis function neural networks (RBFNNs). The stability of system is ensured by the constructed Lyapunov functions. The fractional adaptive laws are proposed to update uncertain parameters. The proposed controller can ensure convergence of the tracking error and all the states remain bounded in the closed-loop systems. Lastly, the feasibility of the proposed control method is proved by giving two examples.

Tracking control of state constrained fractional order nonlinear systems

2021 ◽  
Author(s):  
Changhui Wang ◽  
Xiao Li ◽  
Limin Cui ◽  
Yantao Wang ◽  
Mei Liang ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Fractional Order ◽  
Tracking Control

Passivity-based non-fragile control of a class of uncertain fractional-order nonlinear systems

Integration ◽  
2021 ◽  
Author(s):  
Fei Qi ◽  
Yi Chai ◽  
Liping Chen ◽  
YangQuan Chen ◽  
Ranchao Wu
Keyword(s):  
Nonlinear Systems ◽  
Fractional Order

Compound FAT-based Learning Control of Uncertain Fractional-Order Nonlinear Systems With Disturbance

2021 ◽  
pp. 1-1
Author(s):  
Seyed Mehdi Abedi Pahnehkolaei ◽  
Javad Keighobadi ◽  
Alireza Alfi ◽  
Hamidreza Modares
Keyword(s):  
Nonlinear Systems ◽  
Fractional Order ◽  
Learning Control

Unknown input fractional-order functional observer design for one-side Lipschitz time-delay fractional-order systems

2019 ◽  
Vol 41 (15) ◽  
pp. 4311-4321 ◽  
Author(s):  
Mai Viet Thuan ◽  
Dinh Cong Huong ◽  
Nguyen Huu Sau ◽  
Quan Thai Ha
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Quadratic Function ◽  
Observer Design ◽  
Linear Matrix ◽  
Unknown Input ◽  
Functional Observer ◽  
The One

This paper addresses the problem of unknown input fractional-order functional state observer design for a class of fractional-order time-delay nonlinear systems. The nonlinearities consist of two parts where one part is assumed to satisfy both the one-sided Lipschitz condition and the quadratically inner-bounded condition and the other is not necessary to be Lipschitz and can be regarded as an unknown input, making the wider class of considered nonlinear systems. By taking the advantages of recent results on Caputo fractional derivative of a quadratic function, we derive new sufficient conditions with the form of linear matrix inequalities (LMIs) to guarantee the asymptotic stability of the systems. Four examples are also provided to show the effectiveness and applicability of the proposed method.

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