Exponential stability criteria for neural network based control of nonlinear systems

Author(s):  
Ayush Kumar Jain ◽  
Christophe Fiter ◽  
Denis Berdjag ◽  
Philippe Polet
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Faming Guo ◽  
Ricai Luo ◽  
Xiaolan Qin ◽  
Yunfei Yi

In this paper, we study the problem of exponential stability for the Hopfield neural network with time-varying delays. Different from the existing results, we establish new stability criteria by employing the method of variation of constants and Gronwall’s integral inequality. Finally, we give several examples to show the effectiveness and applicability of the obtained criterion.


2021 ◽  
pp. 002029402110211
Author(s):  
Tao Chen ◽  
Damin Cao ◽  
Jiaxin Yuan ◽  
Hui Yang

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.


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