Persistence of the saddle-node bifurcation for nonlinear systems with slow unmodeled dynamics

1993 ◽  
Vol 12 (4) ◽  
pp. 533-555 ◽  
Author(s):  
Lazhar Fekih-Ahmed ◽  
Hsiao-Dong Chiang
Keyword(s):  
Nonlinear Systems ◽  
Unmodeled Dynamics ◽  
Saddle Node Bifurcation ◽  
Saddle Node

Attractor-preserving control to avoid saddle-node bifurcation

2014 ◽  
Vol 2 ◽  
pp. 150-153
Author(s):  
Daisuke Ito ◽  
Tetsushi Ueta ◽  
Shigeki Tsuji ◽  
Kazuyuki Aihara
Keyword(s):  
Saddle Node Bifurcation ◽  
Saddle Node

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.

Adaptive control of output feedback nonlinear systems with unmodeled dynamics and output constraint

2017 ◽  
Vol 354 (13) ◽  
pp. 5176-5200 ◽  
Author(s):  
Ningning Wang ◽  
Tianping Zhang ◽  
Yang Yi ◽  
Qin Wang
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Output Feedback ◽  
Unmodeled Dynamics ◽  
Output Constraint
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