Delayed Feedback Control for Linear Time-Varying Periodic Systems in Act-and-Wait Fashion

Taib, Mohd Amir Fikri bin Mohd; Hayakawa, Tomohisa; Cetinkaya, Ahmet

doi:10.3182/20130703-3-fr-4039.00041

Cited by 3 publications

(1 citation statement)

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“…The act-and-wait control method is an effective technique to reduce the number of poles for systems with large feedback delay, which makes the pole placement problem easier. In recent years, act-and-wait concept has been further tested through experiments [49] and theoretically extended to discrete-time systems [50], autonomous systems [51], non-autonomous dynamical systems [52], linear periodic time-varying systems [53,54], etc. [55][56][57][58].…”

Section: Introductionmentioning

confidence: 99%

Stabilization of chaotic systems via act-and-wait delayed feedback control using a high-precision direct integration method

Liu

Yan

2020

SN Appl. Sci.

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A technique for the numerical analysis of the stability problem in chaotic systems via act-and-wait delayed feedback control is developed and justified. Recently, act-and-wait modification of a delayed feedback control method is proposed to stabilize unstable periodic orbits in dynamical systems. To overcome the difficulties in obtaining conditions under which the state of closed-loop system converges toward a periodic solution via the act-and-wait scheme, this paper presents a high-precision direct integration method for calculating the monodromy matrix corresponding to the closed-loop system based on the theory of Peano-Baker series. The capabilities of the proposed schemes in stabilization of unstable periodic orbits of chaotic systems are illustrated by numerical examples.

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Section: Introductionmentioning

confidence: 99%

Stabilization of chaotic systems via act-and-wait delayed feedback control using a high-precision direct integration method

Liu

Yan

2020

SN Appl. Sci.

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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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Sampled-data delayed feedback control for stabilizing unstable periodic orbits

Cetinkaya

Hayakawa

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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Delayed Feedback Control for Linear Time-Varying Periodic Systems in Act-and-Wait Fashion

Cited by 3 publications

References 12 publications

Stabilization of chaotic systems via act-and-wait delayed feedback control using a high-precision direct integration method

Stabilization of chaotic systems via act-and-wait delayed feedback control using a high-precision direct integration method

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

Sampled-data delayed feedback control for stabilizing unstable periodic orbits

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