Robust fault-tolerant full-order and reduced-order observer synchronization for differential inclusion chaotic systems with unknown disturbances and parameters

Within the drive-response configuration, this paper considers the synchronization of uncertain chaotic systems based on observers. Even if there are unknown disturbances and parameters in the drive system, a robust adaptive full-order observer can be used to realize chaos synchronization. Further, we develop a reduced-order observer-based response system to synchronize the drive system. By choosing a special reduced-order gain matrix, the reduced-order observer-based response system turns out to be linear and can eliminate the influence of the unknown disturbances and parameters directly. We also discuss the above mentioned two kinds of observers in numerical simulation, and demonstrate that the linear reduced-order observer-based response system is better than the full-order observer-based one.

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Full-order and reduced-order observer-based synchronization for chaotic systems with unknown disturbances and parameters

Physics Letters A ◽

10.1016/j.physleta.2007.06.081 ◽

2008 ◽

Vol 372 (3) ◽

pp. 223-232 ◽

Cited By ~ 45

Author(s):

Fanglai Zhu

Keyword(s):

Chaotic Systems ◽

Reduced Order ◽

Unknown Disturbances ◽

Reduced Order Observer

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Reduced-order observer-based fault estimation and fault-tolerant control for a class of discrete Lipschitz nonlinear systems

Optimal Control Applications and Methods ◽

10.1002/oca.2235 ◽

2016 ◽

Vol 37 (6) ◽

pp. 1236-1262 ◽

Cited By ~ 7

Author(s):

Huaming Qian ◽

Yu Peng ◽

Guangyi Yang

Keyword(s):

Nonlinear Systems ◽

Fault Tolerant ◽

Fault Tolerant Control ◽

Fault Estimation ◽

Reduced Order ◽

Lipschitz Nonlinear Systems ◽

Reduced Order Observer

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Reduced-order observer-based stabilization for the Lur'e differential inclusion system

The 27th Chinese Control and Decision Conference (2015 CCDC) ◽

10.1109/ccdc.2015.7162114 ◽

2015 ◽

Author(s):

Minjie Shi ◽

Jun Huang

Keyword(s):

Differential Inclusion ◽

Reduced Order ◽

Reduced Order Observer

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A new reduced-order observer for the synchronization of nonlinear chaotic systems: An application to secure communications

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/1.4934650 ◽

2015 ◽

Vol 25 (10) ◽

pp. 103128 ◽

Cited By ~ 6

Author(s):

Joel Castro-Ramírez ◽

Rafael Martínez-Guerra ◽

Juan Crescenciano Cruz-Victoria

Keyword(s):

Chaotic Systems ◽

Secure Communications ◽

Reduced Order ◽

Reduced Order Observer

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Adaptive full-order and reduced-order observers for one-sided Lur'e systems with set-valued mappings

IMA Journal of Mathematical Control and Information ◽

10.1093/imamci/dnw066 ◽

2016 ◽

Vol 35 (2) ◽

pp. 569-589 ◽

Cited By ~ 2

Author(s):

Min-Jie Shi ◽

Jun Huang ◽

Liang Chen ◽

Lei Yu

Keyword(s):

Differential Inclusion ◽

Design Method ◽

Rotor System ◽

Observer Design ◽

Adaptive Observer ◽

Unknown Parameters ◽

Lur’E Systems ◽

Reduced Order ◽

Reduced Order Observer ◽

Set Valued Mappings

AbstractThis article proposes an adaptive observer design method for one-sided Lipschitz Lur'e differential inclusion systems with unknown parameters. First, under some assumptions, we design an adaptive full-order observer for the system. Then, under the same assumptions, a reduced-order observer is proved to be valid. Finally, we simulate an example to show the effectiveness of the presented method under the background of rotor system.

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Reduced-order observer design for the synchronization of the generalized Lorenz chaotic systems

Applied Mathematics and Computation ◽

10.1016/j.amc.2012.01.028 ◽

2012 ◽

Vol 218 (14) ◽

pp. 7614-7621 ◽

Cited By ~ 34

Author(s):

Zhengqiang Zhang ◽

Hanyong Shao ◽

Zhen Wang ◽

Hao Shen

Keyword(s):

Chaotic Systems ◽

Observer Design ◽

Reduced Order ◽

Reduced Order Observer

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Observer-Based Synchronization of Chaotic Systems with Both Parameter Uncertainties and Channel Noise

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127414500953 ◽

2014 ◽

Vol 24 (07) ◽

pp. 1450095 ◽

Cited By ~ 2

Author(s):

Xiu Jiang ◽

Junqi Yang ◽

Fanglai Zhu ◽

Liyun Xu

Keyword(s):

Secure Communication ◽

Chaotic Systems ◽

Sliding Mode ◽

High Gain ◽

High Order ◽

Sliding Mode Observer ◽

Channel Noise ◽

Parameter Uncertainties ◽

Reduced Order ◽

Reduced Order Observer

This paper considers observer-based chaos synchronization and chaos-based secure communication problems for a class of uncertain chaotic systems with both parameter uncertainties and channel noise. First, by introducing an augmented vector, the original system is transformed into a new system which has no channel noise. Second, based on the concept of relative degree, an auxiliary drive signal vector is constructed so that the observer matching condition is satisfied. Third, a reduced-order observer is designed to estimate the states of the new augmented system. Then, a high-order high-gain sliding mode observer is considered to estimate the auxiliary drive signals and their derivatives exactly in a finite time. After this, the combination of the reduced-order observer and the high-order high-gain sliding mode observer is used as the receiver in the secure communication mechanism. And a kind of secure information recovery method is developed. Finally, a four-dimensional hyperchaos system is used as the simulation example to illustrate the effectiveness of the proposed methods.

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