Robust digital controllers for uncertain chaotic systems: A digital redesign approach

Ababneh, Mohammad; Barajas-Ramírez, Juan Gonzalo; Chen, Guanrong; Shieh, Leang-San

doi:10.1016/j.chaos.2005.08.217

Cited by 6 publications

(6 citation statements)

References 26 publications

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“…On the other hand, for any , it follows from (5) that (17) For any semi-positive-definite matrix (18) the following holds: (19) where Then, adding the terms on the right-hand side of (14), (16), and (17) to allows us to express as (20) where If and , then for a sufficiently small , which ensures that the origin of the synchronization error system (7) is globally asymptotically stable, i.e., the master system and the slave system in (1) are of global asymptotical synchronization. Setting , , and , and letting , becomes .…”

Section: Resultsmentioning

confidence: 97%

Global Asymptotical Synchronization of Chaotic Lur'e Systems Using Sampled Data: A Linear Matrix Inequality Approach

Hill

2008

IEEE Trans. Circuits Syst. II

108

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Sampled-data feedback control for master-slave synchronization schemes that consist of identical chaotic Lur'e systems is studied. Sufficient conditions for global asymptotic synchronization of such chaotic Lur'e systems are obtained using the free-weighting matrix approach and expressed in terms of linear matrix inequalities (LMIs). With the help of the LMI solvers, the sampled-data feedback control law can easily be obtained to globally asymptotically synchronize Lur'e chaotic systems. The effectiveness of the proposed method is finally illustrated via numerical simulations of chaotic Chua's circuits.

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Section: Resultsmentioning

confidence: 97%

Global Asymptotical Synchronization of Chaotic Lur'e Systems Using Sampled Data: A Linear Matrix Inequality Approach

Hill

2008

IEEE Trans. Circuits Syst. II

108

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“…More transparent and accessible for study is the system generated by (8) According to the classification in [21], at a 12 a 21 > 0, a 12 a 21 < 0 and a 12 a 21 = 0 the system (9) becomes Lorenz, Chen and Lu systems, correspondingly.…”

Section: B a Class Of Superstabilizable Chaotic Systemsmentioning

confidence: 99%

“…While implementing the schemes of the control of chaotic systems we have to face the need of providing specified characteristics of transient behavior and control robustness for various types of perturbations or uncertainties (the inaccuracy of parameter measurements, the influence of external uncontrolled perturbations and so on). As a result there were proposed various methods for controlling chaotic systems with parameter uncertainties: adaptive control method based on the Lyapunov stability theory [7], systematic method for designing robust digital controllers [8], fuzzy control [9][10][11][12], H 2 guaranteed cost fuzzy control [13], and robust fuzzy H ∞ control method [14][15].…”

Section: Introductionmentioning

confidence: 99%

Robust analysis and superstabilization of chaotic systems

Talagaev

2014

2014 IEEE Conference on Control Applications (CCA)

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Superstable behavior is a practically important feature of dynamic systems. In the work we study the peculiarities of superstability achievement as applied to chaotic systems. We show a class of chaotic systems, for which a technique of finding optimal superstabilizing regulators can be presented. The efficiency of superstability conditions for the robust analysis and stabilization in the presence of parametric instability is demonstrated in the work.

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“…The idea of developing a digital controller from a previously designed continuous-time one has been utilized in (Ababneh et al, 2007) , where a controller is designed in terms of the optimal linear model representation of the nominal system around each operating point of the trajectory. Also, digital controllers had been applied to different types of systems, among them are PWM controllers as in (Fujioka et al, 2009), cascaded analog controllers as in (Shieh et al, 1998), where digital redesign method is used to find new pulse-amplitude-modulated (PAM) and pulse-width-modulated (PWM) digital controllers for effective digital control of the analog system, Also delayed systems.…”

Section: Introductionmentioning

confidence: 99%

“…The application of digital redesign to chaotic systems was proposed on earlier works (Ababneh et al, 2007), where designing different digital controllers for uncertain chaotic systems was implemented. However, the problem of applying digital redesign technique to synchronize chaotic systems with uncertainties using fuzzy modeling has not been addressed.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of Chaos Systems Using Fuzzy Logic

Ababneh¹

2011

Journal of Computer Science

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Problem statement: This study presented a new and systematic method to robustly synchronize uncertain chaos systems. It was derived based on the observer approach for synchronization, where error dynamics was made asymptotically stable around the zero to accomplish synchronization. Approach: This method viewed the synchronization problem as a control problem in order to make use of the literature available in this field. In addition, it consisted of designing a digital response system to synchronize with a given continuous-time chaotic drive system. Takagi-Sugeno (TS) fuzzy model was used to model the chaotic dynamic system, while the uncertainties were decomposed such that the uncertain chaotic system could be rewritten as a set of local linear models with an additional disturbed input. Results: This study demonstrated the effectiveness of the methodology presented. The response (receiver) system was able to synchronize very closely with drive (transmitter) system. Furthermore, both piecewise linear and nonlinear uncertain Chua circuits synchronized wonderfully with insignificant errors. Conclusion: The study confirmed that it is capable of achieving excellent synchronization performances, even in the presence of significant parametric uncertainties for uncertain chaos systems. The Takagi-Sugeno (TS) fuzzy model was used to model the chaotic dynamic system, while the uncertainties are decomposed such that the uncertain chaotic system was rewritten as a set of local linear models with an additional disturbed input

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Robust digital controllers for uncertain chaotic systems: A digital redesign approach

Cited by 6 publications

References 26 publications

Global Asymptotical Synchronization of Chaotic Lur'e Systems Using Sampled Data: A Linear Matrix Inequality Approach

Global Asymptotical Synchronization of Chaotic Lur'e Systems Using Sampled Data: A Linear Matrix Inequality Approach

Robust analysis and superstabilization of chaotic systems

Synchronization of Chaos Systems Using Fuzzy Logic

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