On feedback control of chaotic continuous-time systems

Chen, G.; Dong, Xiaoning

doi:10.1109/81.244908

Cited by 417 publications

(126 citation statements)

References 11 publications

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“…Depending on the choice of these constants, it is known that the solutions of (38) may exhibit periodic, almost periodic and chaotic behavior. (period 1), respectively (Chen and Dong, 1993). It is shown that the uncontrolled chaotic dynamic system has different chaotic trajectories with different q values.…”

Section: Simulation Resultsmentioning

confidence: 99%

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Design of Self-Constructing Recurrent-Neural-Network-Based Adaptive Control

Hsu¹,

Lin²

2008

Recurrent Neural Networks

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Section: Simulation Resultsmentioning

confidence: 99%

“…Consider a second-order chaotic system such as the Duffing's equation describing a special nonlinear circuit or a pendulum moving in a viscous medium (Chen and Dong, 1993;Jiang, 2002) …”

Section: Simulation Resultsmentioning

confidence: 99%

Design of Self-Constructing Recurrent-Neural-Network-Based Adaptive Control

Hsu¹,

Lin²

2008

Recurrent Neural Networks

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“…The state trajectory of a chaotic system cannot be predicted due to its sensitivity to initial conditions but, as has been proved, it can be controlled in an efficient way (Ott et al, 1990;Singer et al, 1991;Dressler and Nitsche, 1992;Chen and Dong, 1993;Alsing et al, 1994;Pyragas, 2001;Andrievskii and Fradkov, 2003;Chen et al, 2013;Bashkirtseva and Ryashko, 2013). The term "control of chaos" in this case is considered to be a process of changing irregular and unpredictable behavior to a well-ordered and periodic one.…”

Section: Introductionmentioning

confidence: 99%

Efficiency analysis of control algorithms in spatially distributed systems with chaotic behavior

Korus

2014

International Journal of Applied Mathematics and Computer Science

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The paper presents results of examination of control algorithms for the purpose of controlling chaos in spatially distributed systems like the coupled map lattice (CML). The mathematical definition of the CML, stability analysis as well as some basic results of numerical simulation exposing complex, spatiotemporal and chaotic behavior of the CML were already presented in another paper. The main purpose of this article is to compare the efficiency of controlling chaos by simple classical algorithms in spatially distributed systems like CMLs. This comparison is made based on qualitative and quantitative evaluation methods proposed in the previous paper such as the indirect Lyapunov method, Lyapunov exponents and the net direction phase indicator. As a summary of this paper, some conclusions which can be useful for creating a more efficient algorithm of controlling chaos in spatially distributed systems are made.

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“…Hence, Chaos control problem has been one of the main concerns of researchers wishing to inspect the properties of such systems [5]. Nowadays, many techniques have been proposed to control chaos, including OGY method [6], linear state space feedback [7], adaptive control [8], etc. Some methods are based on knowing the system structure and parameters.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Backstepping Control and Tracking Control for New Chaotic Dynamical System

Zhang¹

2013

IJCCE

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Abstract-Chaos is a very interesting nonlinear phenomenon, and often encountered in many dynamics. Hence, Chaos control problem has been one of the main concerns of researchers wishing to inspect the properties of such systems. This paper focuses on the adaptive control problem and tracking control problem for a new chaotic dynamical system with unknown parameter. Based on a modified backstepping technique and adaptive control method, some chaos controllers are developed for such systems. In comparison with previous methods, the present control technique can improve the speed of parameter identification. The stability analysis in the closed-loop system is given by the Lyapunov method. Finally, numerical simulations are provided to verify the feasibility and effectiveness of the designed controller. Index Terms-Chaos control, adaptive control, backstepping, Lyapunov.

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On feedback control of chaotic continuous-time systems

Cited by 417 publications

References 11 publications

Design of Self-Constructing Recurrent-Neural-Network-Based Adaptive Control

Design of Self-Constructing Recurrent-Neural-Network-Based Adaptive Control

Efficiency analysis of control algorithms in spatially distributed systems with chaotic behavior

Adaptive Backstepping Control and Tracking Control for New Chaotic Dynamical System

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