Delayed feedback control based on the act-and-wait concept

Konishi, Keiji; Kokame, Hideki; Hara, Naoyuki

doi:10.1007/s11071-010-9819-y

Cited by 23 publications

(24 citation statements)

References 39 publications

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“…As a result, we face a problem in which the number of Lyapunov exponents defining the stability of the anticipation manifold is infinite while the number of control parameters in the matrix K is finite. To avoid this difficulty, here we propose to use an act-and-wait concept [21][22][23][24]. The point of the method is that the coupling term with timedelayed feedback is periodically switched on (act) and off (wait).…”

Section: Introductionmentioning

confidence: 99%

Anticipating chaotic synchronization via act-and-wait coupling

Pyragienė

Pyragas

2015

Nonlinear Dyn

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Act-and-wait concept is utilized to design a coupling law for anticipating synchronization of chaotic systems. The time-delay coupling term in this algorithm is periodically switched on and off such that the phase space of the whole system remains finitedimensional despite the presence of the delay. Consequently, the stability of the anticipated synchronization manifold is easily achieved, since it is definite by a finite number of Lyapunov exponents. We show that the stable synchronization regime with considerably large anticipation time can be attained even for single-input single-output systems. The results are demonstrated with the Rössler, Chua and Lorenz chaotic systems.

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Section: Introductionmentioning

confidence: 99%

Anticipating chaotic synchronization via act-and-wait coupling

Pyragienė

Pyragas

2015

Nonlinear Dyn

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“…Act-and-wait concept has been extended to discrete-time systems in [15], and tested through experiments in [16]. Furthermore, act-and-wait approach has been used together with delayed feedback control in [17] for stabilizing unstable fixed points of nonlinear systems, and more recently in [18] for stabilizing unstable periodic orbits of nonautonomous nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Stabilizing unstable periodic orbits with delayed feedback control in act-and-wait fashion

Cetinkaya

Hayakawa

Taib

2018

Systems & Control Letters

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A delayed feedback control framework for stabilizing unstable periodic orbits of linear periodic time-varying systems is proposed. In this framework, act-and-wait approach is utilized for switching a delayed feedback controller on and off alternately at every integer multiples of the period of the system. By analyzing the monodromy matrix of the closed-loop system, we obtain conditions under which the closed-loop system's state converges towards a periodic solution under our proposed control law. We discuss the application of our results in stabilization of unstable periodic orbits of nonlinear systems and present numerical examples to illustrate the efficacy of our approach.

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“…Also, stability of fractional order systems using Lyapunov stability theory has attracted lots of attentions [51,52]. Fractional order controllers have been proposed for many applications such as stabilizing the unstable fixed points of an unstable open-loop system [53], delayed feedback control (DFC) based on the act-and-wait concept for nonlinear dynamical systems [54]. Control and synchronization of an induction motor system are investigated by Chen et al [46][47][48][49][50]55].…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Synchronous Reluctance Motor: Analysis, Chaos Control and FPGA Implementation

Rajagopal

Nazarimehr

Srinivasan³

et al. 2017

Asian Journal of Control

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This paper deals with the dynamical analysis and chaos control in a fractional order synchronous reluctance motor (FOSyncRM). Equilibrium points, characteristic equations and Eigen values of both commensurate and incommensurate FOSyncRM are presented. finite‐time Lyapunov exponents of the FOSyncRM system for fixed and varied parameters are investigated along with the bifurcation plots. Fractional order bifurcation plots are derived to show that the system shows more complex chaotic oscillations in fractional order. Chaos control in the FOSyncRM system is achieved using adaptive sliding mode controllers and the entire control algorithm is implemented in FPGA.

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Delayed feedback control based on the act-and-wait concept

Cited by 23 publications

References 39 publications

Anticipating chaotic synchronization via act-and-wait coupling

Anticipating chaotic synchronization via act-and-wait coupling

Stabilizing unstable periodic orbits with delayed feedback control in act-and-wait fashion

Fractional Order Synchronous Reluctance Motor: Analysis, Chaos Control and FPGA Implementation

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