Synchronization of chaotic systems based on SDRE method

Jayaram, A.; Tadi, M.

doi:10.1016/j.chaos.2005.04.117

Cited by 31 publications

(20 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The chaos represents an interesting topic because irregular oscillations can be undesirable in some physical systems. Control and synchronization schemes for different chaotic systems have been explored by various researchers since long [1][2][3][4][5][6][7][8]. These systems find applications in spread spectrum waveforms, secure communication, cryptography and they are utilized as chaotic sources in transmitter-receiver schemes [9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Observer-based synchronization scheme for a class of chaotic systems using contraction theory

Sharma

Kar

2010

Nonlinear Dyn

View full text Add to dashboard Cite

In this paper, an adaptive synchronization scheme is proposed for a class of nonlinear systems. The design utilizes an adaptive observer, which is quite useful in establishing a transmitter-receiver kind of synchronization scheme. The proposed approach is based on contraction theory and provides a very simple way of establishing exponential convergence of observer states to actual system states. The class of systems addressed here has uncertain parameters, associated with the part of system dynamics that is a function of measurable output only. The explicit conditions for the stability of the observer are derived in terms of gain selection of the observer. Initially, the case without uncertainty is considered and then the results are extended to the case with uncertainty in parameters of the system. An application of the proposed approach is presented to synchronize the family of N chaotic systems which are coupled through the output variable only. The numerical results are presented for designing an adaptive observer for the chaotic Chua system to verify the efficacy of the proposed approach. Explicit bounds on observer gains are derived by exploiting the properties of the chaotic attractor exhibited by Chua's system. Convergence of uncertain parameters is also analyzed for this case and numerical simulations depict the convergence of parameter estimates to their true value.

show abstract

Section: Introductionmentioning

confidence: 99%

Observer-based synchronization scheme for a class of chaotic systems using contraction theory

Sharma

Kar

2010

Nonlinear Dyn

View full text Add to dashboard Cite

show abstract

“…Where a is the parameter of virtual system and parametric error is defined as 1 a a a   .The Jacobian matrix in this case will be 1 1 2…”

Section: Iii2 Observer Design For Chaotic Lorenz System For Parametrmentioning

confidence: 99%

“…Where m  x and ( , ) t fx is continuous differentiable function such that, : ( 1) m f vector function. The main definition and theorem of contraction are taken from [15] and reproduced here for the clarity purpose.…”

Section: Preliminariesmentioning

confidence: 99%

“…Since last few decades, synchronization & stability of chaotic system have been explored by many researchers [1][2][3][4]. Synchronization of two chaotic system means that system trajectories of both the system are varying in synchronized way keeping in view the significant applications of chaotic systems in different fields, many chaotic systems are studied and analyzed.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Simple Observer Based Synchronization of Lorenz System with Parametric Uncertainty

Vaishnav¹

2012

IOSRJEEE

View full text Add to dashboard Cite

“…The purpose of the present work lies in the design of a robust optimal control system for the control and synchronization of new hyperchaotic system using the state-dependent Riccati equation (SDRE) method. The State-Dependent Riccati Equation (SDRE) techniques are general design methods that control problems involving nonlinear systems [10][11][12][13][14]. For a nonlinear system a form of linearization is required which is not an approximation but simply a rewriting of the mathematical model in a different form.…”

Section: Introductionmentioning

confidence: 99%

Control and Synchronization of Hyperchaotic System based on SDRE Method

Ziabari¹,

Sahab

2014

IJIEEB

View full text Add to dashboard Cite

Abstract-In this paper, stabilization and synchronization problems of the hyperchaotic system is investigated. For this reason, state dependent Riccati equation (SDRE) is used. First, stabilizer is designed by SDRE method. Then, robust controller is designed that it can stabilize hyperchaotic system with uncertainly. Finally, synchronization problem between two hyperchaotic systems is considered. The optimal controller is designed that it synchronizes two hyperchaotic systems. Numerical simulation results are presented to show the effectiveness of the proposed controllers.

show abstract

Synchronization of chaotic systems based on SDRE method

Cited by 31 publications

References 14 publications

Observer-based synchronization scheme for a class of chaotic systems using contraction theory

Observer-based synchronization scheme for a class of chaotic systems using contraction theory

Simple Observer Based Synchronization of Lorenz System with Parametric Uncertainty

Control and Synchronization of Hyperchaotic System based on SDRE Method

Contact Info

Product

Resources

About