Hybrid synchronization of n–scroll Chua and Lur’e chaotic systems via backstepping control with novel feedback

Rasappan, Suresh; Vaidyanathan, Sundarapandian

doi:10.2478/v10170-011-0028-9

Cited by 71 publications

(16 citation statements)

References 41 publications

(43 reference statements)

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“…For the GPS of the Wang and Liu systems, we define the GPS synchronization error as We implement the active controller by substitute the control law (35) into the GPS error dynamics (34).…”

Section:  mentioning

confidence: 99%

“…In addition to complete synchronization (CS) of chaotic systems, there are also other types of synchronization of chaotic systems such as anti-synchronization [32][33][34], hybrid synchronization [35][36], projective synchronization [37][38], generalized synchronization [39][40], etc. This paper considers a new type of synchronization problem namely generalized projective synchronization (GPS) [41][42][43] of chaotic systems, which generalizes other types of synchronizations mentioned above like complete synchronization (CS), anti-synchronization (AS), hybrid synchronization (HS), projective synchronization (PS) and generalized synchronization (GS).…”

Section: Introductionmentioning

confidence: 99%

“…Theorem 3. The active control law defined by(35) achieves Proof. We take the candidate Lyapunov function Clearly, V is quadratic and positive definite.…”

mentioning

confidence: 98%

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Active controller design for the GPS of four-wing chaotic systems

Vaidyanathan

Pakiriswamy

2013

2013 Fourth International Conference on Computing, Communications and Networking Technologies (ICCCNT)

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Generalized projective synchronization (GPS) of chaotic systems is a new type of synchronization, which is a general form of synchronization compared to other types of synchronization such as complete synchronization (CS), antisynchronization (AS), hybrid synchronization (HS), projective synchronization (PS), etc. There are many types of techniques available for synchronizing chaotic systems such as delayed feedback control, sampled-data feedback control, sliding mode control, backstepping control, etc. In this paper, we have used active control method for GPS of four-wing chaotic systems, viz. Wang four-wing chaotic system (2009) and Liu four-wing chaotic system (2009). Explicitly, we derive active controllers for GPS of identical Wang four-wing chaotic systems, identical Liu fourwing chaotic systems and non-identical Wang and Liu four-wing chaotic systems. Main GPS results in this work have been proved with the help of Lyapunov stability theory. MATLAB plots are shown to demonstrate the GPS results for Wang and Liu fourwing chaotic systems.

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“…For the GPS of the Wang and Liu systems, we define the GPS synchronization error as We implement the active controller by substitute the control law (35) into the GPS error dynamics (34).…”

Section:  mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Active controller design for the GPS of four-wing chaotic systems

Vaidyanathan

Pakiriswamy

2013

2013 Fourth International Conference on Computing, Communications and Networking Technologies (ICCCNT)

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“…In 1990, a seminal paper on synchronizing two identical chaotic systems was proposed by Pecora and Carroll [46]. This was followed by many different techniques for chaos synchronization in the literature such as active control [47][48][49][50], adaptive control [51][52][53][54], sliding mode control [55][56][57][58], backstepping control [59][60][61][62], sampled-data feedback control [63][64], etc.…”

Section: Introductionmentioning

confidence: 99%

Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperboli c Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters

Vaidyanathan¹

2013

JESTR

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This research work describes the modelling of two novel 3-D chaotic systems, the first with a hyperbolic sinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (A)) and the second with a hyperbolic cosinusoidal nonlinearity and two quadratic nonlinearities (denoted as system (B)). In this work, a detailed qualitative analysis of the novel chaotic systems (A) and (B) has been presented, and the Lyapunov exponents and Kaplan-Yorke dimension of these chaotic systems have been obtained. It is found that the maximal Lyapunov exponent (MLE) for the novel chaotic systems (A) and (B) has a large value, viz. for the system (A) and for the system (B). Thus, both the novel chaotic systems (A) and (B) display strong chaotic behaviour. This research work also discusses the problem of finding adaptive controllers for the global chaos synchronization of identical chaotic systems (A), identical chaotic systems (B) and nonidentical chaotic systems (A) and (B) with unknown system parameters. The adaptive controllers for achieving global chaos synchronization of the novel chaotic systems (A) and (B) have been derived using adaptive control theory and Lyapunov stability theory. MATLAB simulations have been shown to illustrate the novel chaotic systems (A) and (B), and also the adaptive synchronization results derived for the novel chaotic systems (A) and (B).

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“…Many other effective methods and techniques have been developed on the same examples, such as feedback approach [41], sliding-mode [37] and backstepping design technique [26,36].…”

Section: Simulation Studymentioning

confidence: 99%