LMI-based fuzzy chaotic synchronization and communications

Lian, Kuang‐Yow; Chiu, Chian‐Song; Chiang, Tung-Sheng; Liu, P.

doi:10.1109/91.940967

Cited by 132 publications

(9 citation statements)

References 24 publications

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“…In the synchronizations presented so far, we used the T–S fuzzy models provided in Section 5.3 . However, for a given dynamical system, the fuzzy model is not unique [ 42 , 43 ]. A proposal to systematically obtain other T–S fuzzy models is the tensor product (TP) model transformation [ 57 , 58 , 59 ].…”

Section: Simulation Resultsmentioning

confidence: 99%

“…These rules are capable of exactly describing nonlinear systems within some region of interest. Nonlinearities are expressed as inferred fuzzy outputs by indicating the fuzzy membership function in the premise and the associated coefficients in the consequence [ 42 ].…”

Section: Fuzzy Controlmentioning

confidence: 99%

“…The vector function

is expressed as the inferred fuzzy output

in ( 4 ). There exist several ways to implement fuzzy modeling [ 38 , 42 , 43 ]. Here, we chose the one described in [ 42 , 43 ].…”

Section: Fuzzy Controlmentioning

confidence: 99%

“…There exist several ways to implement fuzzy modeling [ 38 , 42 , 43 ]. Here, we chose the one described in [ 42 , 43 ]. Because each chaotic test system has nonlinear terms with a state variable in common, we only need two rules to model them in a fuzzy manner.…”

Section: Fuzzy Controlmentioning

confidence: 99%

“…Substituting the fuzzy control ( 8 ) in the error ( 7 ), one obtains

The gain matrices

are calculated during the design process. With the idea of linearization given in [ 38 , 42 ], if there exists gain matrices such that

then the total error of the system becomes linear when

according to the fuzzy control ( 8 ), where

. Moreover, if

, the the error is asymptotically stable.…”

Section: Fuzzy Synchronizationmentioning

confidence: 99%

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Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Zaqueros-Martinez

Gómez

Tlelo‐Cuautle

et al. 2023

Entropy

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Chaotic systems are hard to synchronize, and no general solution exists. The presence of hidden attractors makes finding a solution particularly elusive. Successful synchronization critically depends on the control strategy, which must be carefully chosen considering system features such as the presence of hidden attractors. We studied the feasibility of fuzzy control for synchronizing chaotic systems with hidden attractors and employed a special numerical integration method that takes advantage of the oscillatory characteristic of chaotic systems. We hypothesized that fuzzy synchronization and the chosen numerical integration method can successfully deal with this case of synchronization. We tested two synchronization schemes: complete synchronization, which leverages linearization, and projective synchronization, capitalizing on parallel distributed compensation (PDC). We applied the proposal to a set of known chaotic systems of integer order with hidden attractors. Our results indicated that fuzzy control strategies combined with the special numerical integration method are effective tools to synchronize chaotic systems with hidden attractors. In addition, for projective synchronization, we propose a new strategy to optimize error convergence. Furthermore, we tested and compared different Takagi–Sugeno (T–S) fuzzy models obtained by tensor product (TP) model transformation. We found an effect of the fuzzy model of the chaotic system on the synchronization performance.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Fuzzy Controlmentioning

confidence: 99%

“…The vector function

is expressed as the inferred fuzzy output

in ( 4 ). There exist several ways to implement fuzzy modeling [ 38 , 42 , 43 ]. Here, we chose the one described in [ 42 , 43 ].…”

Section: Fuzzy Controlmentioning

confidence: 99%

Section: Fuzzy Controlmentioning

confidence: 99%

“…Substituting the fuzzy control ( 8 ) in the error ( 7 ), one obtains

The gain matrices

are calculated during the design process. With the idea of linearization given in [ 38 , 42 ], if there exists gain matrices such that

then the total error of the system becomes linear when

according to the fuzzy control ( 8 ), where

. Moreover, if

, the the error is asymptotically stable.…”

Section: Fuzzy Synchronizationmentioning

confidence: 99%

See 3 more Smart Citations

Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Zaqueros-Martinez

Gómez

Tlelo‐Cuautle

et al. 2023

Entropy

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Synchronization of Time‐Delay Chaotic System with Uncertainties in Terms of Takagi–Sugeno Fuzzy System

Kumaravel

Rasappan

Mohan

2021

Fuzzy Intelligent Systems

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Synchronization of A Class of Uncertain Chaotic Systems with Lipschitz Nonlinearities Using State‐Feedback Control Design: A Matrix Inequality Approach

Mobayen

Tchier

2017

Asian Journal of Control

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This paper proposes a new state-feedback stabilization control technique for a class of uncertain chaotic systems with Lipschitz nonlinearity conditions. Based on Lyapunov stabilization theory and the linear matrix inequality (LMI) scheme, a new sufficient condition formulated in the form of LMIs is created for the chaos synchronization of chaotic systems with parametric uncertainties and external disturbances on the slave system. Using Barbalat's lemma, the suggested approach guarantees that the slave system synchronizes to the master system at an asymptotical convergence rate. Meanwhile, a criterion to find the proper feedback gain vector F is also provided. A new continuous-bounded nonlinear function is introduced to cope with the disturbances and uncertainties and obtain a desired control performance, i.e. small steady-state error and fast settling time. Several criteria are derived to guarantee the asymptotic and robust stability of the uncertain master-slave systems. Furthermore, the proposed controller is independent of the order of the system's model. Numerical simulation results are displayed with an expected satisfactory performance compared to the available methods.

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LMI-based fuzzy chaotic synchronization and communications

Cited by 132 publications

References 24 publications

Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Fuzzy Synchronization of Chaotic Systems with Hidden Attractors

Synchronization of Time‐Delay Chaotic System with Uncertainties in Terms of Takagi–Sugeno Fuzzy System

Synchronization of A Class of Uncertain Chaotic Systems with Lipschitz Nonlinearities Using State‐Feedback Control Design: A Matrix Inequality Approach

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