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

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

doi:10.1016/j.sysconle.2018.01.010

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

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

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	71-77
Number of pages	7
Journal	Systems and Control Letters
Volume	113
DOIs	https://doi.org/10.1016/j.sysconle.2018.01.010
Publication status	Published - 2018 Mar
Externally published	Yes

Keywords

Delayed feedback stabilization
Periodic systems
Stabilization of periodic orbits
Time-varying systems

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science(all)
Mechanical Engineering
Electrical and Electronic Engineering

Access to Document

10.1016/j.sysconle.2018.01.010

Cite this

@article{d10f963dd50349b78542edf8f0cb7ed4,

title = "Stabilizing unstable periodic orbits with delayed feedback control in act-and-wait fashion",

abstract = "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.",

keywords = "Delayed feedback stabilization, Periodic systems, Stabilization of periodic orbits, Time-varying systems",

author = "Ahmet Cetinkaya and Tomohisa Hayakawa and {Mohd Taib}, {Mohd Amir Fikri bin}",

note = "Funding Information: This research was supported by the Aihara Project, the FIRST program from JSPS , initiated by CSTP. Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

year = "2018",

month = mar,

doi = "10.1016/j.sysconle.2018.01.010",

language = "English",

volume = "113",

pages = "71--77",

journal = "Systems and Control Letters",

issn = "0167-6911",

publisher = "Elsevier",

}

TY - JOUR

T1 - Stabilizing unstable periodic orbits with delayed feedback control in act-and-wait fashion

AU - Cetinkaya, Ahmet

AU - Hayakawa, Tomohisa

AU - Mohd Taib, Mohd Amir Fikri bin

PY - 2018/3

Y1 - 2018/3

N2 - 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.

AB - 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.

KW - Delayed feedback stabilization

KW - Periodic systems

KW - Stabilization of periodic orbits

KW - Time-varying systems

UR - http://www.scopus.com/inward/record.url?scp=85041540148&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041540148&partnerID=8YFLogxK

U2 - 10.1016/j.sysconle.2018.01.010

DO - 10.1016/j.sysconle.2018.01.010

M3 - Article

AN - SCOPUS:85041540148

SN - 0167-6911

VL - 113

SP - 71

EP - 77

JO - Systems and Control Letters

JF - Systems and Control Letters

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this