Adaptive controller design for lag-synchronization of two non-identical time-delayed chaotic systems with unknown parameters

Pourdehi, Shabnam; Karimaghaee, Paknosh; Karimipour, Dena

doi:10.1016/j.physleta.2011.02.008

Cited by 19 publications

(14 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(1) and ( 2) are the same dimensions when r = l. The time delays τ i (i = 1, 2) are positive constants which can exist in the well-known chaotic and hyperchaotic systems, including Chen system, Lorenz system, L ü system, hyperchaotic Lozenz system, etc. Then, the synchronization problem for the delayed chaotic systems also has been studied [43][44][45]. However, up to now, there is no paper to investigate the adaptive TVMP synchronization of TDCSs with different dimensions within a fixed time.…”

Section: Remarkmentioning

confidence: 99%

Fixed-Time Adaptive Time-Varying Matrix Projective Synchronization of Time-Delayed Chaotic Systems with Different Dimensions

Zheng¹,

Guo²,

Wen³

2022

Computer Modeling in Engineering &Amp; Sciences

View full text Add to dashboard Cite

This paper deals with the fixed-time adaptive time-varying matrix projective synchronization (ATVMPS) of different dimensional chaotic systems (DDCSs) with time delays and unknown parameters. Firstly, to estimate the unknown parameters, adaptive parameter updated laws are designed. Secondly, to realize the fixed-time ATVMPS of the time-delayed DDCSs, an adaptive delay-unrelated controller is designed, where time delays of chaotic systems are known or unknown. Thirdly, some simple fixed-time ATVMPS criteria are deduced, and the rigorous proof is provided by employing the inequality technique and Lyapunov theory. Furthermore, the settling time of fixed-time synchronization (Fix-TS) is obtained, which depends only on controller parameters and system parameters and is independent of the system's initial states. Finally, simulation examples are presented to validate the theoretical analysis. KEYWORDSTime-varying matrix projective synchronization (TVMPS); fixed-time control; unknown parameters; different dimensions; time-delayed chaotic systems (TDCSs)

show abstract

Section: Remarkmentioning

confidence: 99%

Fixed-Time Adaptive Time-Varying Matrix Projective Synchronization of Time-Delayed Chaotic Systems with Different Dimensions

Zheng¹,

Guo²,

Wen³

2022

Computer Modeling in Engineering &Amp; Sciences

View full text Add to dashboard Cite

show abstract

“…Given two systems in the master-slave configuration, the objective in chaos synchronization is to make the response system variables synchronized in time with the corresponding drive system vari-ables. At the beginning, Pecora and Carroll introduced the concept of complete (identical) synchronization (IS), but, year after year, different types of synchronization have been proposed in the literature, for continuous-and discrete-time systems [3][4][5][6][7][8][9][10]. For example, in projective synchronization (PS) the response system variables are scaled replicas of the drive system variables [11].…”

Section: Introductionmentioning

confidence: 99%

Coexistence of identical synchronization, antiphase synchronization and inverse full state hybrid projective synchronization in different dimensional fractional-order chaotic systems

et al. 2018

View full text Add to dashboard Cite

The topic related to the coexistence of different synchronization types between fractional-order chaotic systems is almost unexplored in the literature. Referring to commensurate and incommensurate fractional systems, this paper presents a new approach to rigorously study the coexistence of some synchronization types between nonidentical systems characterized by different dimensions and different orders. In particular, the paper shows that identical synchronization (IS), antiphase synchronization (AS), and inverse full state hybrid projective synchronization (IFSHPS) coexist when synchronizing a three-dimensional master system with a fourth-dimensional slave system. The approach, which can be applied to a wide class of chaotic/hyperchaotic fractional-order systems in the master-slave configuration, is based on two new theorems involving the fractional Lyapunov method and stability theory of linear fractional systems. Two examples are provided to highlight the capability of the conceived method. In particular, referring to commensurate systems, the coexistence of IS, AS, and IFSHPS is successfully achieved between the chaotic three-dimensional Rössler system of order 2.7 and the hyperchaotic four-dimensional Chen system of order 3.84. Finally, referring to incommensurate systems, the coexistence of IS, AS, and IFSHPS is successfully achieved between the chaotic three-dimensional Lü system of order 2.955 and the hyperchaotic four-dimensional Lorenz system of order 3.86.

show abstract

“…Little over the past two decades various methods for synchronization of chaotic systems have been proposed such as linear and nonlinear feedback synchronization [2][3][4], adaptive feedback control [5], active control [6], optimal control [7], time delay feedback approach [8], sliding mode control [9], backstepping design method [10], tracking control [11] and so on. Due to fast growing interest in chaos synchronization variety of synchronization types and schemes have also been investigated such as complete synchronization [12], phase synchronization [13], antiphase synchronization [14], lag synchronization [15], generalized synchronization [16], antisynchronization [17], projective synchronization [18], function projective synchronization [19],…”

Section: Introductionmentioning

confidence: 99%

Reduced order multi switching hybrid synchronization of chaotic systems

Khan¹,

Khattar²,

Prajapati³

2018

Preprint

View full text Add to dashboard Cite

In this article, a new synchronization scheme is presented by combining the concept of reduced-order synchronization with multi-switching synchronization schemes. The presented scheme, reduced-order multiswitching hybrid synchronization, is notable addition to the earlier multi-switching schemes providing enhanced security in applications of secure communication. Based on the Lyapunov stability theory, the active control method is used to design the controllers and derive sufficient condition for achieving reduced-order multi-switching hybrid synchronization between a new hyperchaotic system taken as drive system and Qi chaotic system serving as response system. Numerical simulations are performed in MATLAB using the Runge-Kutta method to verify the effectiveness of the proposed method. The results show the utility and suitability of the active control method for achieving the reduced-order multi-switching hybrid synchronization among dynamical chaotic systems.

show abstract

Adaptive controller design for lag-synchronization of two non-identical time-delayed chaotic systems with unknown parameters

Cited by 19 publications

References 26 publications

Fixed-Time Adaptive Time-Varying Matrix Projective Synchronization of Time-Delayed Chaotic Systems with Different Dimensions

Fixed-Time Adaptive Time-Varying Matrix Projective Synchronization of Time-Delayed Chaotic Systems with Different Dimensions

Coexistence of identical synchronization, antiphase synchronization and inverse full state hybrid projective synchronization in different dimensional fractional-order chaotic systems

Reduced order multi switching hybrid synchronization of chaotic systems

Contact Info

Product

Resources

About