Master-slave synchronization of continuously and intermittently coupled sampled-data chaotic oscillators

Sang Hoon Lee, Vikram Kapila, Maurizio Porfiri, Anshuman Panda

Research output: Contribution to journalArticle

Abstract

In this paper, we consider the problem of synchronizing a master-slave chaotic system in the sampled-data setting. We consider both the intermittent coupling and continuous coupling cases. We use an Euler approximation technique to discretize a continuous-time chaotic oscillator containing a continuous nonlinear function. Next, we formulate the problem of global asymptotic synchronization of the sampled-data master-slave chaotic system as equivalent to the states of a corresponding error system asymptotically converging to zero for arbitrary initial conditions. We begin by developing a pulse-based intermittent control strategy for chaos synchronization. Using the discrete-time Lyapunov stability theory and the linear matrix inequality (LMI) framework, we construct a state feedback periodic pulse control law which yields global asymptotic synchronization of the sampled-data master-slave chaotic system for arbitrary initial conditions. We obtain a continuously coupled sampled-data feedback control law as a special case of the pulse-based feedback control. Finally, we provide experimental validation of our results by implementing, on a set of microcontrollers endowed with RF communication capability, a sampled-data master-slave chaotic system based on Chua's circuit.

Original languageEnglish (US)
Pages (from-to)4100-4113
Number of pages14
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume15
Issue number12
DOIs
StatePublished - Dec 2010

Fingerprint

Chaotic Oscillator
Chaotic systems
Chaotic System
Synchronization
Feedback Control
Feedback control
Initial conditions
Sampled-data Control
Chua's Circuit
Chaos Synchronization
Microcontroller
Lyapunov Stability Theory
Experimental Validation
Arbitrary
Microcontrollers
Linear matrix inequalities
State feedback
State Feedback
Nonlinear Function
Chaos theory

Keywords

  • Chaos
  • Linear matrix inequality
  • Microcontroller
  • Sampled-data
  • Synchronization

ASJC Scopus subject areas

  • Modeling and Simulation
  • Numerical Analysis
  • Applied Mathematics

Cite this

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title = "Master-slave synchronization of continuously and intermittently coupled sampled-data chaotic oscillators",
abstract = "In this paper, we consider the problem of synchronizing a master-slave chaotic system in the sampled-data setting. We consider both the intermittent coupling and continuous coupling cases. We use an Euler approximation technique to discretize a continuous-time chaotic oscillator containing a continuous nonlinear function. Next, we formulate the problem of global asymptotic synchronization of the sampled-data master-slave chaotic system as equivalent to the states of a corresponding error system asymptotically converging to zero for arbitrary initial conditions. We begin by developing a pulse-based intermittent control strategy for chaos synchronization. Using the discrete-time Lyapunov stability theory and the linear matrix inequality (LMI) framework, we construct a state feedback periodic pulse control law which yields global asymptotic synchronization of the sampled-data master-slave chaotic system for arbitrary initial conditions. We obtain a continuously coupled sampled-data feedback control law as a special case of the pulse-based feedback control. Finally, we provide experimental validation of our results by implementing, on a set of microcontrollers endowed with RF communication capability, a sampled-data master-slave chaotic system based on Chua's circuit.",
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AU - Lee, Sang Hoon

AU - Kapila, Vikram

AU - Porfiri, Maurizio

AU - Panda, Anshuman

PY - 2010/12

Y1 - 2010/12

N2 - In this paper, we consider the problem of synchronizing a master-slave chaotic system in the sampled-data setting. We consider both the intermittent coupling and continuous coupling cases. We use an Euler approximation technique to discretize a continuous-time chaotic oscillator containing a continuous nonlinear function. Next, we formulate the problem of global asymptotic synchronization of the sampled-data master-slave chaotic system as equivalent to the states of a corresponding error system asymptotically converging to zero for arbitrary initial conditions. We begin by developing a pulse-based intermittent control strategy for chaos synchronization. Using the discrete-time Lyapunov stability theory and the linear matrix inequality (LMI) framework, we construct a state feedback periodic pulse control law which yields global asymptotic synchronization of the sampled-data master-slave chaotic system for arbitrary initial conditions. We obtain a continuously coupled sampled-data feedback control law as a special case of the pulse-based feedback control. Finally, we provide experimental validation of our results by implementing, on a set of microcontrollers endowed with RF communication capability, a sampled-data master-slave chaotic system based on Chua's circuit.

AB - In this paper, we consider the problem of synchronizing a master-slave chaotic system in the sampled-data setting. We consider both the intermittent coupling and continuous coupling cases. We use an Euler approximation technique to discretize a continuous-time chaotic oscillator containing a continuous nonlinear function. Next, we formulate the problem of global asymptotic synchronization of the sampled-data master-slave chaotic system as equivalent to the states of a corresponding error system asymptotically converging to zero for arbitrary initial conditions. We begin by developing a pulse-based intermittent control strategy for chaos synchronization. Using the discrete-time Lyapunov stability theory and the linear matrix inequality (LMI) framework, we construct a state feedback periodic pulse control law which yields global asymptotic synchronization of the sampled-data master-slave chaotic system for arbitrary initial conditions. We obtain a continuously coupled sampled-data feedback control law as a special case of the pulse-based feedback control. Finally, we provide experimental validation of our results by implementing, on a set of microcontrollers endowed with RF communication capability, a sampled-data master-slave chaotic system based on Chua's circuit.

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KW - Linear matrix inequality

KW - Microcontroller

KW - Sampled-data

KW - Synchronization

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