scholarly journals Chaotic synchronization of memristive neurons: Lyapunov function versus Hamilton function

2020 ◽  
Vol 101 (1) ◽  
pp. 487-500
Author(s):  
Marius E. Yamakou
Keyword(s):  
Lyapunov Function ◽  
Function Versus ◽  
Chaotic Synchronization ◽  
Hamilton Function ◽  
Lyapunov Function Versus

scholarly journals Chaotic Synchronization of Modified Discrete-Time Tinkerbell Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Ke Ding ◽  
Xing Xu
Keyword(s):  
Feedback Control ◽  
Lyapunov Function ◽  
Discrete Time ◽  
Chaotic Synchronization ◽  
Linear Feedback ◽  
Linear Feedback Control

This paper studies chaotic synchronization of modified discrete-time Tinkerbell systems. By constructing the Lyapunov function and using the linear feedback control, some synchronization criteria for modified discrete-time Tinkerbell systems are derived. The conservativeness of those synchronization criteria is compared. The effectiveness of derived results is demonstrated by six examples.

Sliding observer for synchronization of fractional order chaotic systems with mismatched parameter

Open Physics ◽  
2012 ◽  
Vol 10 (5) ◽  
Author(s):  
Hadi Delavari ◽  
Danial Senejohnny ◽  
Dumitru Baleanu
Keyword(s):  
Lyapunov Function ◽  
Fractional Order ◽  
Canonical Form ◽  
Chaotic System ◽  
Finite Time ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Chaotic Synchronization ◽  
Mode Theory ◽  
Synchronization Scheme

AbstractIn this paper, we propose an observer-based fractional order chaotic synchronization scheme. Our method concerns fractional order chaotic systems in Brunovsky canonical form. Using sliding mode theory, we achieve synchronization of fractional order response with fractional order drive system using a classical Lyapunov function, and also by fractional order differentiation and integration, i.e. differintegration formulas, state synchronization proved to be established in a finite time. To demonstrate the efficiency of the proposed scheme, fractional order version of a well-known chaotic system; Arnodo-Coullet system is considered as illustrative examples.

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.

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