Finite energy Lyapunov function candidate for fractional order general nonlinear systems

2019 ◽  
Vol 78 ◽  
pp. 104886 ◽  
Author(s):  
Yan Li ◽  
Daduan Zhao ◽  
YangQuan Chen ◽  
Igor Podlubny ◽  
Chenghui Zhang
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Fractional Order ◽  
Finite Energy

Adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics

2021 ◽  
pp. 014233122098563
Author(s):  
Fei Shen ◽  
Xinjun Wang ◽  
Xinghui Yin
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Dead Zone ◽  
Small Neighborhood ◽  
Unmodeled Dynamics ◽  
Stochastic Nonlinear Systems ◽  
Dynamic Surface ◽  
Barrier Lyapunov Function ◽  
Full State

This paper investigates the problem of adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics. To stabilize such a system, a dynamic signal is introduced to dominate unmodeled dynamics and an assistant signal is constructed to compensate for the effect of the dead zone. Dynamic surface control is used to solve the “complexity explosion” problem in traditional backstepping design. Two cases of symmetric and asymmetric Barrier Lyapunov functions are discussed respectively in this paper. The proposed Barrier Lyapunov function based on backstepping method can ensure that the output tracking error converges in the small neighborhood of the origin. This control scheme can ensure that semi-globally uniformly ultimately boundedness of all signals in the closed-loop system. Two simulation cases are proposed to verify the effectiveness of the theoretical method.

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

Robust stability and memory state feedback control for a class of switched nonlinear systems with multiple time-varying delays

2021 ◽  
pp. 107754632098598
Author(s):  
Marwen Kermani ◽  
Anis Sakly
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Feedback Stabilization ◽  
State Feedback Control ◽  
Multiple Time ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Common Lyapunov Function ◽  
Suggested Approach ◽  
Aggregation Techniques

This study is concerned with the stability analysis and the feedback stabilization problems for a class of uncertain switched nonlinear systems with multiple time-varying delays. Unusually, more general time delays, which depend on the subsystem number, are considered. In this regard, by constructing a novel common Lyapunov function, using the aggregation techniques and the Borne and Gentina criterion, new algebraic stability and feedback stabilization conditions under arbitrary switching are derived. The proposed results are explicit and obtained without searching a common Lyapunov function through the linear matrix inequalities approach, considered a difficult matter in this case. At last, two numerical simulation examples are shown to prove the practical utility of the suggested approach.

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
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